[{"data":1,"prerenderedAt":4991},["ShallowReactive",2],{"post-\u002Fblog\u002Fliniyni-rivnyannya-7-klas":3,"post-rel-\u002Fblog\u002Fliniyni-rivnyannya-7-klas":4986},{"id":4,"title":5,"body":6,"date":4968,"description":4969,"draft":4970,"extension":4971,"grade":360,"image":4972,"meta":4973,"navigation":4974,"path":4975,"rawbody":4976,"seo":4977,"stem":4978,"subject":39,"tags":4979,"topic":4984,"updated":4972,"__hash__":4985},"blog\u002Fblog\u002Fliniyni-rivnyannya-7-klas.md","Лінійні рівняння з однією змінною, 7 клас: пояснення з прикладами",{"type":7,"value":8,"toc":4952},"minimark",[9,13,18,25,119,415,421,425,457,1149,1153,1213,1227,1230,1272,1276,1358,1396,1595,1697,1701,1824,1827,2158,2363,2367,2572,2603,2803,2807,3110,3174,3178,3363,3369,3373,3379,3514,3812,3817,3821,4331,4335,4470],[10,11,12],"p",{},"Лінійні рівняння — фундамент усієї шкільної алгебри. Якщо добре зрозуміти цю тему в 7 класі, то квадратні рівняння, системи й нерівності далі підуть набагато легше.",[14,15,17],"h2",{"id":16},"що-таке-лінійне-рівняння","Що таке лінійне рівняння",[10,19,20,24],{},[21,22,23],"strong",{},"Лінійним рівнянням з однією змінною"," називають рівняння виду",[26,27,30],"span",{"className":28},[29],"katex-display",[26,31,34,72],{"className":32},[33],"katex",[26,35,38],{"className":36},[37],"katex-mathml",[39,40,43],"math",{"xmlns":41,"display":42},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[44,45,46,67],"semantics",{},[47,48,49,53,56,60,63],"mrow",{},[50,51,52],"mi",{},"a",[50,54,55],{},"x",[57,58,59],"mo",{},"=",[50,61,62],{},"b",[57,64,66],{"separator":65},"true",",",[68,69,71],"annotation",{"encoding":70},"application\u002Fx-tex","ax = b,",[26,73,76,105],{"className":74,"ariaHidden":65},[75],"katex-html",[26,77,80,85,90,93,98,102],{"className":78},[79],"base",[26,81],{"className":82,"style":84},[83],"strut","height:0.4306em;",[26,86,52],{"className":87},[88,89],"mord","mathnormal",[26,91,55],{"className":92},[88,89],[26,94],{"className":95,"style":97},[96],"mspace","margin-right:0.2778em;",[26,99,59],{"className":100},[101],"mrel",[26,103],{"className":104,"style":97},[96],[26,106,108,112,115],{"className":107},[79],[26,109],{"className":110,"style":111},[83],"height:0.8889em;vertical-align:-0.1944em;",[26,113,62],{"className":114},[88,89],[26,116,66],{"className":117},[118],"mpunct",[10,120,121,122,150,151,179,180,209,210,270,271,270,336,414],{},"де ",[26,123,125,138],{"className":124},[33],[26,126,128],{"className":127},[37],[39,129,130],{"xmlns":41},[44,131,132,136],{},[47,133,134],{},[50,135,55],{},[68,137,55],{"encoding":70},[26,139,141],{"className":140,"ariaHidden":65},[75],[26,142,144,147],{"className":143},[79],[26,145],{"className":146,"style":84},[83],[26,148,55],{"className":149},[88,89]," — змінна, а ",[26,152,154,167],{"className":153},[33],[26,155,157],{"className":156},[37],[39,158,159],{"xmlns":41},[44,160,161,165],{},[47,162,163],{},[50,164,52],{},[68,166,52],{"encoding":70},[26,168,170],{"className":169,"ariaHidden":65},[75],[26,171,173,176],{"className":172},[79],[26,174],{"className":175,"style":84},[83],[26,177,52],{"className":178},[88,89]," і ",[26,181,183,196],{"className":182},[33],[26,184,186],{"className":185},[37],[39,187,188],{"xmlns":41},[44,189,190,194],{},[47,191,192],{},[50,193,62],{},[68,195,62],{"encoding":70},[26,197,199],{"className":198,"ariaHidden":65},[75],[26,200,202,206],{"className":201},[79],[26,203],{"className":204,"style":205},[83],"height:0.6944em;",[26,207,62],{"className":208},[88,89]," — числа. Наприклад: ",[26,211,213,236],{"className":212},[33],[26,214,216],{"className":215},[37],[39,217,218],{"xmlns":41},[44,219,220,233],{},[47,221,222,226,228,230],{},[223,224,225],"mn",{},"3",[50,227,55],{},[57,229,59],{},[223,231,232],{},"12",[68,234,235],{"encoding":70},"3x = 12",[26,237,239,261],{"className":238,"ariaHidden":65},[75],[26,240,242,246,249,252,255,258],{"className":241},[79],[26,243],{"className":244,"style":245},[83],"height:0.6444em;",[26,247,225],{"className":248},[88],[26,250,55],{"className":251},[88,89],[26,253],{"className":254,"style":97},[96],[26,256,59],{"className":257},[101],[26,259],{"className":260,"style":97},[96],[26,262,264,267],{"className":263},[79],[26,265],{"className":266,"style":245},[83],[26,268,232],{"className":269},[88],", ",[26,272,274,299],{"className":273},[33],[26,275,277],{"className":276},[37],[39,278,279],{"xmlns":41},[44,280,281,296],{},[47,282,283,286,289,291,293],{},[57,284,285],{},"−",[223,287,288],{},"2",[50,290,55],{},[57,292,59],{},[223,294,295],{},"5",[68,297,298],{"encoding":70},"-2x = 5",[26,300,302,327],{"className":301,"ariaHidden":65},[75],[26,303,305,309,312,315,318,321,324],{"className":304},[79],[26,306],{"className":307,"style":308},[83],"height:0.7278em;vertical-align:-0.0833em;",[26,310,285],{"className":311},[88],[26,313,288],{"className":314},[88],[26,316,55],{"className":317},[88,89],[26,319],{"className":320,"style":97},[96],[26,322,59],{"className":323},[101],[26,325],{"className":326,"style":97},[96],[26,328,330,333],{"className":329},[79],[26,331],{"className":332,"style":245},[83],[26,334,295],{"className":335},[88],[26,337,339,364],{"className":338},[33],[26,340,342],{"className":341},[37],[39,343,344],{"xmlns":41},[44,345,346,361],{},[47,347,348,351,354,356,358],{},[223,349,350],{},"0",[57,352,353],{},"⋅",[50,355,55],{},[57,357,59],{},[223,359,360],{},"7",[68,362,363],{"encoding":70},"0 \\cdot x = 7",[26,365,367,387,405],{"className":366,"ariaHidden":65},[75],[26,368,370,373,376,380,384],{"className":369},[79],[26,371],{"className":372,"style":245},[83],[26,374,350],{"className":375},[88],[26,377],{"className":378,"style":379},[96],"margin-right:0.2222em;",[26,381,353],{"className":382},[383],"mbin",[26,385],{"className":386,"style":379},[96],[26,388,390,393,396,399,402],{"className":389},[79],[26,391],{"className":392,"style":84},[83],[26,394,55],{"className":395},[88,89],[26,397],{"className":398,"style":97},[96],[26,400,59],{"className":401},[101],[26,403],{"className":404,"style":97},[96],[26,406,408,411],{"className":407},[79],[26,409],{"className":410,"style":245},[83],[26,412,360],{"className":413},[88],".",[10,416,417,420],{},[21,418,419],{},"Корінь рівняння"," — це значення змінної, при якому рівняння перетворюється на правильну числову рівність. Розв’язати рівняння — означає знайти всі його корені або довести, що їх немає.",[14,422,424],{"id":423},"скільки-коренів-може-бути","Скільки коренів може бути",[10,426,427,428,456],{},"Усе залежить від коефіцієнта ",[26,429,431,444],{"className":430},[33],[26,432,434],{"className":433},[37],[39,435,436],{"xmlns":41},[44,437,438,442],{},[47,439,440],{},[50,441,52],{},[68,443,52],{"encoding":70},[26,445,447],{"className":446,"ariaHidden":65},[75],[26,448,450,453],{"className":449},[79],[26,451],{"className":452,"style":84},[83],[26,454,52],{"className":455},[88,89],":",[458,459,460,476],"table",{},[461,462,463],"thead",{},[464,465,466,470,473],"tr",{},[467,468,469],"th",{},"Випадок",[467,471,472],{},"Що отримуємо",[467,474,475],{},"Коренів",[477,478,479,719,932],"tbody",{},[464,480,481,577,716],{},[482,483,484],"td",{},[26,485,487,507],{"className":486},[33],[26,488,490],{"className":489},[37],[39,491,492],{"xmlns":41},[44,493,494,504],{},[47,495,496,498,502],{},[50,497,52],{},[57,499,501],{"mathvariant":500},"normal","≠",[223,503,350],{},[68,505,506],{"encoding":70},"a \\ne 0",[26,508,510,568],{"className":509,"ariaHidden":65},[75],[26,511,513,516,519,522,565],{"className":512},[79],[26,514],{"className":515,"style":111},[83],[26,517,52],{"className":518},[88,89],[26,520],{"className":521,"style":97},[96],[26,523,525,558,562],{"className":524},[101],[26,526,528],{"className":527},[101],[26,529,532],{"className":530},[88,531],"vbox",[26,533,536],{"className":534},[535],"thinbox",[26,537,540,543,554],{"className":538},[539],"rlap",[26,541],{"className":542,"style":111},[83],[26,544,547],{"className":545},[546],"inner",[26,548,550],{"className":549},[88],[26,551,553],{"className":552},[101],"",[26,555],{"className":556},[557],"fix",[26,559],{"className":560},[96,561],"nobreak",[26,563,59],{"className":564},[101],[26,566],{"className":567,"style":97},[96],[26,569,571,574],{"className":570},[79],[26,572],{"className":573,"style":245},[83],[26,575,350],{"className":576},[88],[482,578,579],{},[26,580,582,608],{"className":581},[33],[26,583,585],{"className":584},[37],[39,586,587],{"xmlns":41},[44,588,589,605],{},[47,590,591,593,595],{},[50,592,55],{},[57,594,59],{},[596,597,598],"mstyle",{"scriptlevel":350,"displaystyle":65},[599,600,601,603],"mfrac",{},[50,602,62],{},[50,604,52],{},[68,606,607],{"encoding":70},"x = \\dfrac{b}{a}",[26,609,611,629],{"className":610,"ariaHidden":65},[75],[26,612,614,617,620,623,626],{"className":613},[79],[26,615],{"className":616,"style":84},[83],[26,618,55],{"className":619},[88,89],[26,621],{"className":622,"style":97},[96],[26,624,59],{"className":625},[101],[26,627],{"className":628,"style":97},[96],[26,630,632,636],{"className":631},[79],[26,633],{"className":634,"style":635},[83],"height:2.0574em;vertical-align:-0.686em;",[26,637,639,644,712],{"className":638},[88],[26,640],{"className":641},[642,643],"mopen","nulldelimiter",[26,645,647],{"className":646},[599],[26,648,652,703],{"className":649},[650,651],"vlist-t","vlist-t2",[26,653,656,698],{"className":654},[655],"vlist-r",[26,657,661,675,686],{"className":658,"style":660},[659],"vlist","height:1.3714em;",[26,662,664,669],{"style":663},"top:-2.314em;",[26,665],{"className":666,"style":668},[667],"pstrut","height:3em;",[26,670,672],{"className":671},[88],[26,673,52],{"className":674},[88,89],[26,676,678,681],{"style":677},"top:-3.23em;",[26,679],{"className":680,"style":668},[667],[26,682],{"className":683,"style":685},[684],"frac-line","border-bottom-width:0.04em;",[26,687,689,692],{"style":688},"top:-3.677em;",[26,690],{"className":691,"style":668},[667],[26,693,695],{"className":694},[88],[26,696,62],{"className":697},[88,89],[26,699,702],{"className":700},[701],"vlist-s","​",[26,704,706],{"className":705},[655],[26,707,710],{"className":708,"style":709},[659],"height:0.686em;",[26,711],{},[26,713],{"className":714},[715,643],"mclose",[482,717,718],{},"один",[464,720,721,825,929],{},[482,722,723,270,774],{},[26,724,726,744],{"className":725},[33],[26,727,729],{"className":728},[37],[39,730,731],{"xmlns":41},[44,732,733,741],{},[47,734,735,737,739],{},[50,736,52],{},[57,738,59],{},[223,740,350],{},[68,742,743],{"encoding":70},"a = 0",[26,745,747,765],{"className":746,"ariaHidden":65},[75],[26,748,750,753,756,759,762],{"className":749},[79],[26,751],{"className":752,"style":84},[83],[26,754,52],{"className":755},[88,89],[26,757],{"className":758,"style":97},[96],[26,760,59],{"className":761},[101],[26,763],{"className":764,"style":97},[96],[26,766,768,771],{"className":767},[79],[26,769],{"className":770,"style":245},[83],[26,772,350],{"className":773},[88],[26,775,777,795],{"className":776},[33],[26,778,780],{"className":779},[37],[39,781,782],{"xmlns":41},[44,783,784,792],{},[47,785,786,788,790],{},[50,787,62],{},[57,789,59],{},[223,791,350],{},[68,793,794],{"encoding":70},"b = 0",[26,796,798,816],{"className":797,"ariaHidden":65},[75],[26,799,801,804,807,810,813],{"className":800},[79],[26,802],{"className":803,"style":205},[83],[26,805,62],{"className":806},[88,89],[26,808],{"className":809,"style":97},[96],[26,811,59],{"className":812},[101],[26,814],{"className":815,"style":97},[96],[26,817,819,822],{"className":818},[79],[26,820],{"className":821,"style":245},[83],[26,823,350],{"className":824},[88],[482,826,827,900,901],{},[26,828,830,852],{"className":829},[33],[26,831,833],{"className":832},[37],[39,834,835],{"xmlns":41},[44,836,837,849],{},[47,838,839,841,843,845,847],{},[223,840,350],{},[57,842,353],{},[50,844,55],{},[57,846,59],{},[223,848,350],{},[68,850,851],{"encoding":70},"0 \\cdot x = 0",[26,853,855,873,891],{"className":854,"ariaHidden":65},[75],[26,856,858,861,864,867,870],{"className":857},[79],[26,859],{"className":860,"style":245},[83],[26,862,350],{"className":863},[88],[26,865],{"className":866,"style":379},[96],[26,868,353],{"className":869},[383],[26,871],{"className":872,"style":379},[96],[26,874,876,879,882,885,888],{"className":875},[79],[26,877],{"className":878,"style":84},[83],[26,880,55],{"className":881},[88,89],[26,883],{"className":884,"style":97},[96],[26,886,59],{"className":887},[101],[26,889],{"className":890,"style":97},[96],[26,892,894,897],{"className":893},[79],[26,895],{"className":896,"style":245},[83],[26,898,350],{"className":899},[88]," — правильно для будь-якого ",[26,902,904,917],{"className":903},[33],[26,905,907],{"className":906},[37],[39,908,909],{"xmlns":41},[44,910,911,915],{},[47,912,913],{},[50,914,55],{},[68,916,55],{"encoding":70},[26,918,920],{"className":919,"ariaHidden":65},[75],[26,921,923,926],{"className":922},[79],[26,924],{"className":925,"style":84},[83],[26,927,55],{"className":928},[88,89],[482,930,931],{},"безліч",[464,933,934,1070,1146],{},[482,935,936,270,986],{},[26,937,939,956],{"className":938},[33],[26,940,942],{"className":941},[37],[39,943,944],{"xmlns":41},[44,945,946,954],{},[47,947,948,950,952],{},[50,949,52],{},[57,951,59],{},[223,953,350],{},[68,955,743],{"encoding":70},[26,957,959,977],{"className":958,"ariaHidden":65},[75],[26,960,962,965,968,971,974],{"className":961},[79],[26,963],{"className":964,"style":84},[83],[26,966,52],{"className":967},[88,89],[26,969],{"className":970,"style":97},[96],[26,972,59],{"className":973},[101],[26,975],{"className":976,"style":97},[96],[26,978,980,983],{"className":979},[79],[26,981],{"className":982,"style":245},[83],[26,984,350],{"className":985},[88],[26,987,989,1007],{"className":988},[33],[26,990,992],{"className":991},[37],[39,993,994],{"xmlns":41},[44,995,996,1004],{},[47,997,998,1000,1002],{},[50,999,62],{},[57,1001,501],{"mathvariant":500},[223,1003,350],{},[68,1005,1006],{"encoding":70},"b \\ne 0",[26,1008,1010,1061],{"className":1009,"ariaHidden":65},[75],[26,1011,1013,1016,1019,1022,1058],{"className":1012},[79],[26,1014],{"className":1015,"style":111},[83],[26,1017,62],{"className":1018},[88,89],[26,1020],{"className":1021,"style":97},[96],[26,1023,1025,1052,1055],{"className":1024},[101],[26,1026,1028],{"className":1027},[101],[26,1029,1031],{"className":1030},[88,531],[26,1032,1034],{"className":1033},[535],[26,1035,1037,1040,1049],{"className":1036},[539],[26,1038],{"className":1039,"style":111},[83],[26,1041,1043],{"className":1042},[546],[26,1044,1046],{"className":1045},[88],[26,1047,553],{"className":1048},[101],[26,1050],{"className":1051},[557],[26,1053],{"className":1054},[96,561],[26,1056,59],{"className":1057},[101],[26,1059],{"className":1060,"style":97},[96],[26,1062,1064,1067],{"className":1063},[79],[26,1065],{"className":1066,"style":245},[83],[26,1068,350],{"className":1069},[88],[482,1071,1072,1145],{},[26,1073,1075,1097],{"className":1074},[33],[26,1076,1078],{"className":1077},[37],[39,1079,1080],{"xmlns":41},[44,1081,1082,1094],{},[47,1083,1084,1086,1088,1090,1092],{},[223,1085,350],{},[57,1087,353],{},[50,1089,55],{},[57,1091,59],{},[50,1093,62],{},[68,1095,1096],{"encoding":70},"0 \\cdot x = b",[26,1098,1100,1118,1136],{"className":1099,"ariaHidden":65},[75],[26,1101,1103,1106,1109,1112,1115],{"className":1102},[79],[26,1104],{"className":1105,"style":245},[83],[26,1107,350],{"className":1108},[88],[26,1110],{"className":1111,"style":379},[96],[26,1113,353],{"className":1114},[383],[26,1116],{"className":1117,"style":379},[96],[26,1119,1121,1124,1127,1130,1133],{"className":1120},[79],[26,1122],{"className":1123,"style":84},[83],[26,1125,55],{"className":1126},[88,89],[26,1128],{"className":1129,"style":97},[96],[26,1131,59],{"className":1132},[101],[26,1134],{"className":1135,"style":97},[96],[26,1137,1139,1142],{"className":1138},[79],[26,1140],{"className":1141,"style":205},[83],[26,1143,62],{"className":1144},[88,89]," — неможливо",[482,1147,1148],{},"немає",[14,1150,1152],{"id":1151},"два-головні-правила","Два головні правила",[10,1154,1155,1156,1212],{},"Щоб звести будь-яке рівняння до вигляду ",[26,1157,1159,1179],{"className":1158},[33],[26,1160,1162],{"className":1161},[37],[39,1163,1164],{"xmlns":41},[44,1165,1166,1176],{},[47,1167,1168,1170,1172,1174],{},[50,1169,52],{},[50,1171,55],{},[57,1173,59],{},[50,1175,62],{},[68,1177,1178],{"encoding":70},"ax = b",[26,1180,1182,1203],{"className":1181,"ariaHidden":65},[75],[26,1183,1185,1188,1191,1194,1197,1200],{"className":1184},[79],[26,1186],{"className":1187,"style":84},[83],[26,1189,52],{"className":1190},[88,89],[26,1192,55],{"className":1193},[88,89],[26,1195],{"className":1196,"style":97},[96],[26,1198,59],{"className":1199},[101],[26,1201],{"className":1202,"style":97},[96],[26,1204,1206,1209],{"className":1205},[79],[26,1207],{"className":1208,"style":205},[83],[26,1210,62],{"className":1211},[88,89],", користуємося двома властивостями:",[1214,1215,1216,1222],"ol",{},[1217,1218,1219],"li",{},[21,1220,1221],{},"Будь-який доданок можна перенести з однієї частини рівняння в іншу, змінивши його знак.",[1217,1223,1224],{},[21,1225,1226],{},"Обидві частини рівняння можна помножити або поділити на одне й те саме число, яке не дорівнює нулю.",[10,1228,1229],{},"Алгоритм розв’язування:",[1214,1231,1232,1235,1238,1241],{},[1217,1233,1234],{},"Розкрити дужки.",[1217,1236,1237],{},"Перенести доданки зі змінною вліво, числа — вправо.",[1217,1239,1240],{},"Звести подібні доданки.",[1217,1242,1243,1244,414],{},"Поділити обидві частини на коефіцієнт при ",[26,1245,1247,1260],{"className":1246},[33],[26,1248,1250],{"className":1249},[37],[39,1251,1252],{"xmlns":41},[44,1253,1254,1258],{},[47,1255,1256],{},[50,1257,55],{},[68,1259,55],{"encoding":70},[26,1261,1263],{"className":1262,"ariaHidden":65},[75],[26,1264,1266,1269],{"className":1265},[79],[26,1267],{"className":1268,"style":84},[83],[26,1270,55],{"className":1271},[88,89],[14,1273,1275],{"id":1274},"приклад-1-найпростіший","Приклад 1. Найпростіший",[26,1277,1279],{"className":1278},[29],[26,1280,1282,1307],{"className":1281},[33],[26,1283,1285],{"className":1284},[37],[39,1286,1287],{"xmlns":41,"display":42},[44,1288,1289,1304],{},[47,1290,1291,1293,1295,1297,1299,1301],{},[223,1292,225],{},[50,1294,55],{},[57,1296,285],{},[223,1298,360],{},[57,1300,59],{},[223,1302,1303],{},"8",[68,1305,1306],{"encoding":70},"3x - 7 = 8",[26,1308,1310,1331,1349],{"className":1309,"ariaHidden":65},[75],[26,1311,1313,1316,1319,1322,1325,1328],{"className":1312},[79],[26,1314],{"className":1315,"style":308},[83],[26,1317,225],{"className":1318},[88],[26,1320,55],{"className":1321},[88,89],[26,1323],{"className":1324,"style":379},[96],[26,1326,285],{"className":1327},[383],[26,1329],{"className":1330,"style":379},[96],[26,1332,1334,1337,1340,1343,1346],{"className":1333},[79],[26,1335],{"className":1336,"style":245},[83],[26,1338,360],{"className":1339},[88],[26,1341],{"className":1342,"style":97},[96],[26,1344,59],{"className":1345},[101],[26,1347],{"className":1348,"style":97},[96],[26,1350,1352,1355],{"className":1351},[79],[26,1353],{"className":1354,"style":245},[83],[26,1356,1303],{"className":1357},[88],[10,1359,1360,1361,1395],{},"Переносимо ",[26,1362,1364,1380],{"className":1363},[33],[26,1365,1367],{"className":1366},[37],[39,1368,1369],{"xmlns":41},[44,1370,1371,1377],{},[47,1372,1373,1375],{},[57,1374,285],{},[223,1376,360],{},[68,1378,1379],{"encoding":70},"-7",[26,1381,1383],{"className":1382,"ariaHidden":65},[75],[26,1384,1386,1389,1392],{"className":1385},[79],[26,1387],{"className":1388,"style":308},[83],[26,1390,285],{"className":1391},[88],[26,1393,360],{"className":1394},[88]," вправо зі зміною знака:",[26,1397,1399],{"className":1398},[29],[26,1400,1402,1456],{"className":1401},[33],[26,1403,1405],{"className":1404},[37],[39,1406,1407],{"xmlns":41,"display":42},[44,1408,1409,1453],{},[47,1410,1411,1413,1415,1417,1419,1422,1424,1427,1430,1432,1434,1436,1438,1441,1443,1445,1447,1449,1451],{},[223,1412,225],{},[50,1414,55],{},[57,1416,59],{},[223,1418,1303],{},[57,1420,1421],{},"+",[223,1423,360],{},[96,1425],{"width":1426},"1em",[57,1428,1429],{},"⇒",[96,1431],{"width":1426},[223,1433,225],{},[50,1435,55],{},[57,1437,59],{},[223,1439,1440],{},"15",[96,1442],{"width":1426},[57,1444,1429],{},[96,1446],{"width":1426},[50,1448,55],{},[57,1450,59],{},[223,1452,295],{},[68,1454,1455],{"encoding":70},"3x = 8 + 7 \\quad\\Rightarrow\\quad 3x = 15 \\quad\\Rightarrow\\quad x = 5",[26,1457,1459,1480,1498,1523,1544,1568,1586],{"className":1458,"ariaHidden":65},[75],[26,1460,1462,1465,1468,1471,1474,1477],{"className":1461},[79],[26,1463],{"className":1464,"style":245},[83],[26,1466,225],{"className":1467},[88],[26,1469,55],{"className":1470},[88,89],[26,1472],{"className":1473,"style":97},[96],[26,1475,59],{"className":1476},[101],[26,1478],{"className":1479,"style":97},[96],[26,1481,1483,1486,1489,1492,1495],{"className":1482},[79],[26,1484],{"className":1485,"style":308},[83],[26,1487,1303],{"className":1488},[88],[26,1490],{"className":1491,"style":379},[96],[26,1493,1421],{"className":1494},[383],[26,1496],{"className":1497,"style":379},[96],[26,1499,1501,1504,1507,1511,1514,1517,1520],{"className":1500},[79],[26,1502],{"className":1503,"style":245},[83],[26,1505,360],{"className":1506},[88],[26,1508],{"className":1509,"style":1510},[96],"margin-right:1em;",[26,1512],{"className":1513,"style":97},[96],[26,1515,1429],{"className":1516},[101],[26,1518],{"className":1519,"style":1510},[96],[26,1521],{"className":1522,"style":97},[96],[26,1524,1526,1529,1532,1535,1538,1541],{"className":1525},[79],[26,1527],{"className":1528,"style":245},[83],[26,1530,225],{"className":1531},[88],[26,1533,55],{"className":1534},[88,89],[26,1536],{"className":1537,"style":97},[96],[26,1539,59],{"className":1540},[101],[26,1542],{"className":1543,"style":97},[96],[26,1545,1547,1550,1553,1556,1559,1562,1565],{"className":1546},[79],[26,1548],{"className":1549,"style":245},[83],[26,1551,1440],{"className":1552},[88],[26,1554],{"className":1555,"style":1510},[96],[26,1557],{"className":1558,"style":97},[96],[26,1560,1429],{"className":1561},[101],[26,1563],{"className":1564,"style":1510},[96],[26,1566],{"className":1567,"style":97},[96],[26,1569,1571,1574,1577,1580,1583],{"className":1570},[79],[26,1572],{"className":1573,"style":84},[83],[26,1575,55],{"className":1576},[88,89],[26,1578],{"className":1579,"style":97},[96],[26,1581,59],{"className":1582},[101],[26,1584],{"className":1585,"style":97},[96],[26,1587,1589,1592],{"className":1588},[79],[26,1590],{"className":1591,"style":245},[83],[26,1593,295],{"className":1594},[88],[10,1596,1597,1600,1601,1696],{},[21,1598,1599],{},"Перевірка:"," ",[26,1602,1604,1630],{"className":1603},[33],[26,1605,1607],{"className":1606},[37],[39,1608,1609],{"xmlns":41},[44,1610,1611,1627],{},[47,1612,1613,1615,1617,1619,1621,1623,1625],{},[223,1614,225],{},[57,1616,353],{},[223,1618,295],{},[57,1620,285],{},[223,1622,360],{},[57,1624,59],{},[223,1626,1303],{},[68,1628,1629],{"encoding":70},"3 \\cdot 5 - 7 = 8",[26,1631,1633,1651,1669,1687],{"className":1632,"ariaHidden":65},[75],[26,1634,1636,1639,1642,1645,1648],{"className":1635},[79],[26,1637],{"className":1638,"style":245},[83],[26,1640,225],{"className":1641},[88],[26,1643],{"className":1644,"style":379},[96],[26,1646,353],{"className":1647},[383],[26,1649],{"className":1650,"style":379},[96],[26,1652,1654,1657,1660,1663,1666],{"className":1653},[79],[26,1655],{"className":1656,"style":308},[83],[26,1658,295],{"className":1659},[88],[26,1661],{"className":1662,"style":379},[96],[26,1664,285],{"className":1665},[383],[26,1667],{"className":1668,"style":379},[96],[26,1670,1672,1675,1678,1681,1684],{"className":1671},[79],[26,1673],{"className":1674,"style":245},[83],[26,1676,360],{"className":1677},[88],[26,1679],{"className":1680,"style":97},[96],[26,1682,59],{"className":1683},[101],[26,1685],{"className":1686,"style":97},[96],[26,1688,1690,1693],{"className":1689},[79],[26,1691],{"className":1692,"style":245},[83],[26,1694,1303],{"className":1695},[88],". ✓",[14,1698,1700],{"id":1699},"приклад-2-з-дужками","Приклад 2. З дужками",[26,1702,1704],{"className":1703},[29],[26,1705,1707,1745],{"className":1706},[33],[26,1708,1710],{"className":1709},[37],[39,1711,1712],{"xmlns":41,"display":42},[44,1713,1714,1742],{},[47,1715,1716,1718,1722,1724,1726,1728,1731,1733,1735,1737,1739],{},[223,1717,295],{},[57,1719,1721],{"stretchy":1720},"false","(",[50,1723,55],{},[57,1725,285],{},[223,1727,288],{},[57,1729,1730],{"stretchy":1720},")",[57,1732,59],{},[223,1734,288],{},[50,1736,55],{},[57,1738,1421],{},[223,1740,1741],{},"11",[68,1743,1744],{"encoding":70},"5(x - 2) = 2x + 11",[26,1746,1748,1773,1794,1815],{"className":1747,"ariaHidden":65},[75],[26,1749,1751,1755,1758,1761,1764,1767,1770],{"className":1750},[79],[26,1752],{"className":1753,"style":1754},[83],"height:1em;vertical-align:-0.25em;",[26,1756,295],{"className":1757},[88],[26,1759,1721],{"className":1760},[642],[26,1762,55],{"className":1763},[88,89],[26,1765],{"className":1766,"style":379},[96],[26,1768,285],{"className":1769},[383],[26,1771],{"className":1772,"style":379},[96],[26,1774,1776,1779,1782,1785,1788,1791],{"className":1775},[79],[26,1777],{"className":1778,"style":1754},[83],[26,1780,288],{"className":1781},[88],[26,1783,1730],{"className":1784},[715],[26,1786],{"className":1787,"style":97},[96],[26,1789,59],{"className":1790},[101],[26,1792],{"className":1793,"style":97},[96],[26,1795,1797,1800,1803,1806,1809,1812],{"className":1796},[79],[26,1798],{"className":1799,"style":308},[83],[26,1801,288],{"className":1802},[88],[26,1804,55],{"className":1805},[88,89],[26,1807],{"className":1808,"style":379},[96],[26,1810,1421],{"className":1811},[383],[26,1813],{"className":1814,"style":379},[96],[26,1816,1818,1821],{"className":1817},[79],[26,1819],{"className":1820,"style":245},[83],[26,1822,1741],{"className":1823},[88],[10,1825,1826],{},"Розкриваємо дужки і переносимо:",[26,1828,1830],{"className":1829},[29],[26,1831,1833,1915],{"className":1832},[33],[26,1834,1836],{"className":1835},[37],[39,1837,1838],{"xmlns":41,"display":42},[44,1839,1840,1912],{},[47,1841,1842,1844,1846,1848,1851,1853,1855,1857,1859,1861,1863,1865,1867,1869,1871,1873,1875,1877,1879,1881,1883,1885,1887,1889,1891,1893,1895,1897,1900,1902,1904,1906,1908,1910],{},[223,1843,295],{},[50,1845,55],{},[57,1847,285],{},[223,1849,1850],{},"10",[57,1852,59],{},[223,1854,288],{},[50,1856,55],{},[57,1858,1421],{},[223,1860,1741],{},[96,1862],{"width":1426},[57,1864,1429],{},[96,1866],{"width":1426},[223,1868,295],{},[50,1870,55],{},[57,1872,285],{},[223,1874,288],{},[50,1876,55],{},[57,1878,59],{},[223,1880,1741],{},[57,1882,1421],{},[223,1884,1850],{},[96,1886],{"width":1426},[57,1888,1429],{},[96,1890],{"width":1426},[223,1892,225],{},[50,1894,55],{},[57,1896,59],{},[223,1898,1899],{},"21",[96,1901],{"width":1426},[57,1903,1429],{},[96,1905],{"width":1426},[50,1907,55],{},[57,1909,59],{},[223,1911,360],{},[68,1913,1914],{"encoding":70},"5x - 10 = 2x + 11 \\quad\\Rightarrow\\quad 5x - 2x = 11 + 10 \\quad\\Rightarrow\\quad 3x = 21 \\quad\\Rightarrow\\quad x = 7",[26,1916,1918,1939,1957,1978,2002,2023,2044,2062,2086,2107,2131,2149],{"className":1917,"ariaHidden":65},[75],[26,1919,1921,1924,1927,1930,1933,1936],{"className":1920},[79],[26,1922],{"className":1923,"style":308},[83],[26,1925,295],{"className":1926},[88],[26,1928,55],{"className":1929},[88,89],[26,1931],{"className":1932,"style":379},[96],[26,1934,285],{"className":1935},[383],[26,1937],{"className":1938,"style":379},[96],[26,1940,1942,1945,1948,1951,1954],{"className":1941},[79],[26,1943],{"className":1944,"style":245},[83],[26,1946,1850],{"className":1947},[88],[26,1949],{"className":1950,"style":97},[96],[26,1952,59],{"className":1953},[101],[26,1955],{"className":1956,"style":97},[96],[26,1958,1960,1963,1966,1969,1972,1975],{"className":1959},[79],[26,1961],{"className":1962,"style":308},[83],[26,1964,288],{"className":1965},[88],[26,1967,55],{"className":1968},[88,89],[26,1970],{"className":1971,"style":379},[96],[26,1973,1421],{"className":1974},[383],[26,1976],{"className":1977,"style":379},[96],[26,1979,1981,1984,1987,1990,1993,1996,1999],{"className":1980},[79],[26,1982],{"className":1983,"style":245},[83],[26,1985,1741],{"className":1986},[88],[26,1988],{"className":1989,"style":1510},[96],[26,1991],{"className":1992,"style":97},[96],[26,1994,1429],{"className":1995},[101],[26,1997],{"className":1998,"style":1510},[96],[26,2000],{"className":2001,"style":97},[96],[26,2003,2005,2008,2011,2014,2017,2020],{"className":2004},[79],[26,2006],{"className":2007,"style":308},[83],[26,2009,295],{"className":2010},[88],[26,2012,55],{"className":2013},[88,89],[26,2015],{"className":2016,"style":379},[96],[26,2018,285],{"className":2019},[383],[26,2021],{"className":2022,"style":379},[96],[26,2024,2026,2029,2032,2035,2038,2041],{"className":2025},[79],[26,2027],{"className":2028,"style":245},[83],[26,2030,288],{"className":2031},[88],[26,2033,55],{"className":2034},[88,89],[26,2036],{"className":2037,"style":97},[96],[26,2039,59],{"className":2040},[101],[26,2042],{"className":2043,"style":97},[96],[26,2045,2047,2050,2053,2056,2059],{"className":2046},[79],[26,2048],{"className":2049,"style":308},[83],[26,2051,1741],{"className":2052},[88],[26,2054],{"className":2055,"style":379},[96],[26,2057,1421],{"className":2058},[383],[26,2060],{"className":2061,"style":379},[96],[26,2063,2065,2068,2071,2074,2077,2080,2083],{"className":2064},[79],[26,2066],{"className":2067,"style":245},[83],[26,2069,1850],{"className":2070},[88],[26,2072],{"className":2073,"style":1510},[96],[26,2075],{"className":2076,"style":97},[96],[26,2078,1429],{"className":2079},[101],[26,2081],{"className":2082,"style":1510},[96],[26,2084],{"className":2085,"style":97},[96],[26,2087,2089,2092,2095,2098,2101,2104],{"className":2088},[79],[26,2090],{"className":2091,"style":245},[83],[26,2093,225],{"className":2094},[88],[26,2096,55],{"className":2097},[88,89],[26,2099],{"className":2100,"style":97},[96],[26,2102,59],{"className":2103},[101],[26,2105],{"className":2106,"style":97},[96],[26,2108,2110,2113,2116,2119,2122,2125,2128],{"className":2109},[79],[26,2111],{"className":2112,"style":245},[83],[26,2114,1899],{"className":2115},[88],[26,2117],{"className":2118,"style":1510},[96],[26,2120],{"className":2121,"style":97},[96],[26,2123,1429],{"className":2124},[101],[26,2126],{"className":2127,"style":1510},[96],[26,2129],{"className":2130,"style":97},[96],[26,2132,2134,2137,2140,2143,2146],{"className":2133},[79],[26,2135],{"className":2136,"style":84},[83],[26,2138,55],{"className":2139},[88,89],[26,2141],{"className":2142,"style":97},[96],[26,2144,59],{"className":2145},[101],[26,2147],{"className":2148,"style":97},[96],[26,2150,2152,2155],{"className":2151},[79],[26,2153],{"className":2154,"style":245},[83],[26,2156,360],{"className":2157},[88],[10,2159,2160,1600,2162,179,2268,1696],{},[21,2161,1599],{},[26,2163,2165,2196],{"className":2164},[33],[26,2166,2168],{"className":2167},[37],[39,2169,2170],{"xmlns":41},[44,2171,2172,2193],{},[47,2173,2174,2176,2178,2180,2182,2184,2186,2188,2190],{},[223,2175,295],{},[57,2177,353],{},[57,2179,1721],{"stretchy":1720},[223,2181,360],{},[57,2183,285],{},[223,2185,288],{},[57,2187,1730],{"stretchy":1720},[57,2189,59],{},[223,2191,2192],{},"25",[68,2194,2195],{"encoding":70},"5 \\cdot (7 - 2) = 25",[26,2197,2199,2217,2238,2259],{"className":2198,"ariaHidden":65},[75],[26,2200,2202,2205,2208,2211,2214],{"className":2201},[79],[26,2203],{"className":2204,"style":245},[83],[26,2206,295],{"className":2207},[88],[26,2209],{"className":2210,"style":379},[96],[26,2212,353],{"className":2213},[383],[26,2215],{"className":2216,"style":379},[96],[26,2218,2220,2223,2226,2229,2232,2235],{"className":2219},[79],[26,2221],{"className":2222,"style":1754},[83],[26,2224,1721],{"className":2225},[642],[26,2227,360],{"className":2228},[88],[26,2230],{"className":2231,"style":379},[96],[26,2233,285],{"className":2234},[383],[26,2236],{"className":2237,"style":379},[96],[26,2239,2241,2244,2247,2250,2253,2256],{"className":2240},[79],[26,2242],{"className":2243,"style":1754},[83],[26,2245,288],{"className":2246},[88],[26,2248,1730],{"className":2249},[715],[26,2251],{"className":2252,"style":97},[96],[26,2254,59],{"className":2255},[101],[26,2257],{"className":2258,"style":97},[96],[26,2260,2262,2265],{"className":2261},[79],[26,2263],{"className":2264,"style":245},[83],[26,2266,2192],{"className":2267},[88],[26,2269,2271,2297],{"className":2270},[33],[26,2272,2274],{"className":2273},[37],[39,2275,2276],{"xmlns":41},[44,2277,2278,2294],{},[47,2279,2280,2282,2284,2286,2288,2290,2292],{},[223,2281,288],{},[57,2283,353],{},[223,2285,360],{},[57,2287,1421],{},[223,2289,1741],{},[57,2291,59],{},[223,2293,2192],{},[68,2295,2296],{"encoding":70},"2 \\cdot 7 + 11 = 25",[26,2298,2300,2318,2336,2354],{"className":2299,"ariaHidden":65},[75],[26,2301,2303,2306,2309,2312,2315],{"className":2302},[79],[26,2304],{"className":2305,"style":245},[83],[26,2307,288],{"className":2308},[88],[26,2310],{"className":2311,"style":379},[96],[26,2313,353],{"className":2314},[383],[26,2316],{"className":2317,"style":379},[96],[26,2319,2321,2324,2327,2330,2333],{"className":2320},[79],[26,2322],{"className":2323,"style":308},[83],[26,2325,360],{"className":2326},[88],[26,2328],{"className":2329,"style":379},[96],[26,2331,1421],{"className":2332},[383],[26,2334],{"className":2335,"style":379},[96],[26,2337,2339,2342,2345,2348,2351],{"className":2338},[79],[26,2340],{"className":2341,"style":245},[83],[26,2343,1741],{"className":2344},[88],[26,2346],{"className":2347,"style":97},[96],[26,2349,59],{"className":2350},[101],[26,2352],{"className":2353,"style":97},[96],[26,2355,2357,2360],{"className":2356},[79],[26,2358],{"className":2359,"style":245},[83],[26,2361,2192],{"className":2362},[88],[14,2364,2366],{"id":2365},"приклад-3-з-дробами","Приклад 3. З дробами",[26,2368,2370],{"className":2369},[29],[26,2371,2373,2404],{"className":2372},[33],[26,2374,2376],{"className":2375},[37],[39,2377,2378],{"xmlns":41,"display":42},[44,2379,2380,2401],{},[47,2381,2382,2388,2390,2397,2399],{},[599,2383,2384,2386],{},[50,2385,55],{},[223,2387,225],{},[57,2389,1421],{},[599,2391,2392,2394],{},[50,2393,55],{},[223,2395,2396],{},"4",[57,2398,59],{},[223,2400,360],{},[68,2402,2403],{"encoding":70},"\\frac{x}{3} + \\frac{x}{4} = 7",[26,2405,2407,2486,2563],{"className":2406,"ariaHidden":65},[75],[26,2408,2410,2414,2477,2480,2483],{"className":2409},[79],[26,2411],{"className":2412,"style":2413},[83],"height:1.7936em;vertical-align:-0.686em;",[26,2415,2417,2420,2474],{"className":2416},[88],[26,2418],{"className":2419},[642,643],[26,2421,2423],{"className":2422},[599],[26,2424,2426,2466],{"className":2425},[650,651],[26,2427,2429,2463],{"className":2428},[655],[26,2430,2433,2444,2452],{"className":2431,"style":2432},[659],"height:1.1076em;",[26,2434,2435,2438],{"style":663},[26,2436],{"className":2437,"style":668},[667],[26,2439,2441],{"className":2440},[88],[26,2442,225],{"className":2443},[88],[26,2445,2446,2449],{"style":677},[26,2447],{"className":2448,"style":668},[667],[26,2450],{"className":2451,"style":685},[684],[26,2453,2454,2457],{"style":688},[26,2455],{"className":2456,"style":668},[667],[26,2458,2460],{"className":2459},[88],[26,2461,55],{"className":2462},[88,89],[26,2464,702],{"className":2465},[701],[26,2467,2469],{"className":2468},[655],[26,2470,2472],{"className":2471,"style":709},[659],[26,2473],{},[26,2475],{"className":2476},[715,643],[26,2478],{"className":2479,"style":379},[96],[26,2481,1421],{"className":2482},[383],[26,2484],{"className":2485,"style":379},[96],[26,2487,2489,2492,2554,2557,2560],{"className":2488},[79],[26,2490],{"className":2491,"style":2413},[83],[26,2493,2495,2498,2551],{"className":2494},[88],[26,2496],{"className":2497},[642,643],[26,2499,2501],{"className":2500},[599],[26,2502,2504,2543],{"className":2503},[650,651],[26,2505,2507,2540],{"className":2506},[655],[26,2508,2510,2521,2529],{"className":2509,"style":2432},[659],[26,2511,2512,2515],{"style":663},[26,2513],{"className":2514,"style":668},[667],[26,2516,2518],{"className":2517},[88],[26,2519,2396],{"className":2520},[88],[26,2522,2523,2526],{"style":677},[26,2524],{"className":2525,"style":668},[667],[26,2527],{"className":2528,"style":685},[684],[26,2530,2531,2534],{"style":688},[26,2532],{"className":2533,"style":668},[667],[26,2535,2537],{"className":2536},[88],[26,2538,55],{"className":2539},[88,89],[26,2541,702],{"className":2542},[701],[26,2544,2546],{"className":2545},[655],[26,2547,2549],{"className":2548,"style":709},[659],[26,2550],{},[26,2552],{"className":2553},[715,643],[26,2555],{"className":2556,"style":97},[96],[26,2558,59],{"className":2559},[101],[26,2561],{"className":2562,"style":97},[96],[26,2564,2566,2569],{"className":2565},[79],[26,2567],{"className":2568,"style":245},[83],[26,2570,360],{"className":2571},[88],[10,2573,2574,2575,456],{},"Позбуваємося знаменників: множимо обидві частини на спільний знаменник ",[26,2576,2578,2591],{"className":2577},[33],[26,2579,2581],{"className":2580},[37],[39,2582,2583],{"xmlns":41},[44,2584,2585,2589],{},[47,2586,2587],{},[223,2588,232],{},[68,2590,232],{"encoding":70},[26,2592,2594],{"className":2593,"ariaHidden":65},[75],[26,2595,2597,2600],{"className":2596},[79],[26,2598],{"className":2599,"style":245},[83],[26,2601,232],{"className":2602},[88],[26,2604,2606],{"className":2605},[29],[26,2607,2609,2662],{"className":2608},[33],[26,2610,2612],{"className":2611},[37],[39,2613,2614],{"xmlns":41,"display":42},[44,2615,2616,2659],{},[47,2617,2618,2620,2622,2624,2626,2628,2630,2633,2635,2637,2639,2641,2643,2645,2647,2649,2651,2653,2655,2657],{},[223,2619,2396],{},[50,2621,55],{},[57,2623,1421],{},[223,2625,225],{},[50,2627,55],{},[57,2629,59],{},[223,2631,2632],{},"84",[96,2634],{"width":1426},[57,2636,1429],{},[96,2638],{"width":1426},[223,2640,360],{},[50,2642,55],{},[57,2644,59],{},[223,2646,2632],{},[96,2648],{"width":1426},[57,2650,1429],{},[96,2652],{"width":1426},[50,2654,55],{},[57,2656,59],{},[223,2658,232],{},[68,2660,2661],{"encoding":70},"4x + 3x = 84 \\quad\\Rightarrow\\quad 7x = 84 \\quad\\Rightarrow\\quad x = 12",[26,2663,2665,2686,2707,2731,2752,2776,2794],{"className":2664,"ariaHidden":65},[75],[26,2666,2668,2671,2674,2677,2680,2683],{"className":2667},[79],[26,2669],{"className":2670,"style":308},[83],[26,2672,2396],{"className":2673},[88],[26,2675,55],{"className":2676},[88,89],[26,2678],{"className":2679,"style":379},[96],[26,2681,1421],{"className":2682},[383],[26,2684],{"className":2685,"style":379},[96],[26,2687,2689,2692,2695,2698,2701,2704],{"className":2688},[79],[26,2690],{"className":2691,"style":245},[83],[26,2693,225],{"className":2694},[88],[26,2696,55],{"className":2697},[88,89],[26,2699],{"className":2700,"style":97},[96],[26,2702,59],{"className":2703},[101],[26,2705],{"className":2706,"style":97},[96],[26,2708,2710,2713,2716,2719,2722,2725,2728],{"className":2709},[79],[26,2711],{"className":2712,"style":245},[83],[26,2714,2632],{"className":2715},[88],[26,2717],{"className":2718,"style":1510},[96],[26,2720],{"className":2721,"style":97},[96],[26,2723,1429],{"className":2724},[101],[26,2726],{"className":2727,"style":1510},[96],[26,2729],{"className":2730,"style":97},[96],[26,2732,2734,2737,2740,2743,2746,2749],{"className":2733},[79],[26,2735],{"className":2736,"style":245},[83],[26,2738,360],{"className":2739},[88],[26,2741,55],{"className":2742},[88,89],[26,2744],{"className":2745,"style":97},[96],[26,2747,59],{"className":2748},[101],[26,2750],{"className":2751,"style":97},[96],[26,2753,2755,2758,2761,2764,2767,2770,2773],{"className":2754},[79],[26,2756],{"className":2757,"style":245},[83],[26,2759,2632],{"className":2760},[88],[26,2762],{"className":2763,"style":1510},[96],[26,2765],{"className":2766,"style":97},[96],[26,2768,1429],{"className":2769},[101],[26,2771],{"className":2772,"style":1510},[96],[26,2774],{"className":2775,"style":97},[96],[26,2777,2779,2782,2785,2788,2791],{"className":2778},[79],[26,2780],{"className":2781,"style":84},[83],[26,2783,55],{"className":2784},[88,89],[26,2786],{"className":2787,"style":97},[96],[26,2789,59],{"className":2790},[101],[26,2792],{"className":2793,"style":97},[96],[26,2795,2797,2800],{"className":2796},[79],[26,2798],{"className":2799,"style":245},[83],[26,2801,232],{"className":2802},[88],[14,2804,2806],{"id":2805},"приклад-4-коренів-безліч","Приклад 4. Коренів безліч",[26,2808,2810],{"className":2809},[29],[26,2811,2813,2888],{"className":2812},[33],[26,2814,2816],{"className":2815},[37],[39,2817,2818],{"xmlns":41,"display":42},[44,2819,2820,2885],{},[47,2821,2822,2824,2826,2828,2830,2832,2834,2836,2838,2840,2842,2845,2847,2849,2851,2853,2855,2857,2859,2861,2863,2865,2867,2869,2871,2873,2875,2877,2879,2881,2883],{},[223,2823,288],{},[57,2825,1721],{"stretchy":1720},[50,2827,55],{},[57,2829,1421],{},[223,2831,225],{},[57,2833,1730],{"stretchy":1720},[57,2835,59],{},[223,2837,288],{},[50,2839,55],{},[57,2841,1421],{},[223,2843,2844],{},"6",[96,2846],{"width":1426},[57,2848,1429],{},[96,2850],{"width":1426},[223,2852,288],{},[50,2854,55],{},[57,2856,1421],{},[223,2858,2844],{},[57,2860,59],{},[223,2862,288],{},[50,2864,55],{},[57,2866,1421],{},[223,2868,2844],{},[96,2870],{"width":1426},[57,2872,1429],{},[96,2874],{"width":1426},[223,2876,350],{},[57,2878,353],{},[50,2880,55],{},[57,2882,59],{},[223,2884,350],{},[68,2886,2887],{"encoding":70},"2(x + 3) = 2x + 6 \\quad\\Rightarrow\\quad 2x + 6 = 2x + 6 \\quad\\Rightarrow\\quad 0 \\cdot x = 0",[26,2889,2891,2915,2936,2957,2981,3002,3020,3041,3065,3083,3101],{"className":2890,"ariaHidden":65},[75],[26,2892,2894,2897,2900,2903,2906,2909,2912],{"className":2893},[79],[26,2895],{"className":2896,"style":1754},[83],[26,2898,288],{"className":2899},[88],[26,2901,1721],{"className":2902},[642],[26,2904,55],{"className":2905},[88,89],[26,2907],{"className":2908,"style":379},[96],[26,2910,1421],{"className":2911},[383],[26,2913],{"className":2914,"style":379},[96],[26,2916,2918,2921,2924,2927,2930,2933],{"className":2917},[79],[26,2919],{"className":2920,"style":1754},[83],[26,2922,225],{"className":2923},[88],[26,2925,1730],{"className":2926},[715],[26,2928],{"className":2929,"style":97},[96],[26,2931,59],{"className":2932},[101],[26,2934],{"className":2935,"style":97},[96],[26,2937,2939,2942,2945,2948,2951,2954],{"className":2938},[79],[26,2940],{"className":2941,"style":308},[83],[26,2943,288],{"className":2944},[88],[26,2946,55],{"className":2947},[88,89],[26,2949],{"className":2950,"style":379},[96],[26,2952,1421],{"className":2953},[383],[26,2955],{"className":2956,"style":379},[96],[26,2958,2960,2963,2966,2969,2972,2975,2978],{"className":2959},[79],[26,2961],{"className":2962,"style":245},[83],[26,2964,2844],{"className":2965},[88],[26,2967],{"className":2968,"style":1510},[96],[26,2970],{"className":2971,"style":97},[96],[26,2973,1429],{"className":2974},[101],[26,2976],{"className":2977,"style":1510},[96],[26,2979],{"className":2980,"style":97},[96],[26,2982,2984,2987,2990,2993,2996,2999],{"className":2983},[79],[26,2985],{"className":2986,"style":308},[83],[26,2988,288],{"className":2989},[88],[26,2991,55],{"className":2992},[88,89],[26,2994],{"className":2995,"style":379},[96],[26,2997,1421],{"className":2998},[383],[26,3000],{"className":3001,"style":379},[96],[26,3003,3005,3008,3011,3014,3017],{"className":3004},[79],[26,3006],{"className":3007,"style":245},[83],[26,3009,2844],{"className":3010},[88],[26,3012],{"className":3013,"style":97},[96],[26,3015,59],{"className":3016},[101],[26,3018],{"className":3019,"style":97},[96],[26,3021,3023,3026,3029,3032,3035,3038],{"className":3022},[79],[26,3024],{"className":3025,"style":308},[83],[26,3027,288],{"className":3028},[88],[26,3030,55],{"className":3031},[88,89],[26,3033],{"className":3034,"style":379},[96],[26,3036,1421],{"className":3037},[383],[26,3039],{"className":3040,"style":379},[96],[26,3042,3044,3047,3050,3053,3056,3059,3062],{"className":3043},[79],[26,3045],{"className":3046,"style":245},[83],[26,3048,2844],{"className":3049},[88],[26,3051],{"className":3052,"style":1510},[96],[26,3054],{"className":3055,"style":97},[96],[26,3057,1429],{"className":3058},[101],[26,3060],{"className":3061,"style":1510},[96],[26,3063],{"className":3064,"style":97},[96],[26,3066,3068,3071,3074,3077,3080],{"className":3067},[79],[26,3069],{"className":3070,"style":245},[83],[26,3072,350],{"className":3073},[88],[26,3075],{"className":3076,"style":379},[96],[26,3078,353],{"className":3079},[383],[26,3081],{"className":3082,"style":379},[96],[26,3084,3086,3089,3092,3095,3098],{"className":3085},[79],[26,3087],{"className":3088,"style":84},[83],[26,3090,55],{"className":3091},[88,89],[26,3093],{"className":3094,"style":97},[96],[26,3096,59],{"className":3097},[101],[26,3099],{"className":3100,"style":97},[96],[26,3102,3104,3107],{"className":3103},[79],[26,3105],{"className":3106,"style":245},[83],[26,3108,350],{"className":3109},[88],[10,3111,3112,3113,3141,3142,1600,3145,3173],{},"Рівність правильна при будь-якому ",[26,3114,3116,3129],{"className":3115},[33],[26,3117,3119],{"className":3118},[37],[39,3120,3121],{"xmlns":41},[44,3122,3123,3127],{},[47,3124,3125],{},[50,3126,55],{},[68,3128,55],{"encoding":70},[26,3130,3132],{"className":3131,"ariaHidden":65},[75],[26,3133,3135,3138],{"className":3134},[79],[26,3136],{"className":3137,"style":84},[83],[26,3139,55],{"className":3140},[88,89],". ",[21,3143,3144],{},"Відповідь:",[26,3146,3148,3161],{"className":3147},[33],[26,3149,3151],{"className":3150},[37],[39,3152,3153],{"xmlns":41},[44,3154,3155,3159],{},[47,3156,3157],{},[50,3158,55],{},[68,3160,55],{"encoding":70},[26,3162,3164],{"className":3163,"ariaHidden":65},[75],[26,3165,3167,3170],{"className":3166},[79],[26,3168],{"className":3169,"style":84},[83],[26,3171,55],{"className":3172},[88,89]," — будь-яке число.",[14,3175,3177],{"id":3176},"приклад-5-коренів-немає","Приклад 5. Коренів немає",[26,3179,3181],{"className":3180},[29],[26,3182,3184,3231],{"className":3183},[33],[26,3185,3187],{"className":3186},[37],[39,3188,3189],{"xmlns":41,"display":42},[44,3190,3191,3228],{},[47,3192,3193,3195,3197,3199,3202,3204,3206,3208,3210,3212,3214,3216,3218,3220,3222,3224,3226],{},[223,3194,2396],{},[50,3196,55],{},[57,3198,285],{},[223,3200,3201],{},"1",[57,3203,59],{},[223,3205,2396],{},[50,3207,55],{},[57,3209,1421],{},[223,3211,295],{},[96,3213],{"width":1426},[57,3215,1429],{},[96,3217],{"width":1426},[223,3219,350],{},[57,3221,353],{},[50,3223,55],{},[57,3225,59],{},[223,3227,2844],{},[68,3229,3230],{"encoding":70},"4x - 1 = 4x + 5 \\quad\\Rightarrow\\quad 0 \\cdot x = 6",[26,3232,3234,3255,3273,3294,3318,3336,3354],{"className":3233,"ariaHidden":65},[75],[26,3235,3237,3240,3243,3246,3249,3252],{"className":3236},[79],[26,3238],{"className":3239,"style":308},[83],[26,3241,2396],{"className":3242},[88],[26,3244,55],{"className":3245},[88,89],[26,3247],{"className":3248,"style":379},[96],[26,3250,285],{"className":3251},[383],[26,3253],{"className":3254,"style":379},[96],[26,3256,3258,3261,3264,3267,3270],{"className":3257},[79],[26,3259],{"className":3260,"style":245},[83],[26,3262,3201],{"className":3263},[88],[26,3265],{"className":3266,"style":97},[96],[26,3268,59],{"className":3269},[101],[26,3271],{"className":3272,"style":97},[96],[26,3274,3276,3279,3282,3285,3288,3291],{"className":3275},[79],[26,3277],{"className":3278,"style":308},[83],[26,3280,2396],{"className":3281},[88],[26,3283,55],{"className":3284},[88,89],[26,3286],{"className":3287,"style":379},[96],[26,3289,1421],{"className":3290},[383],[26,3292],{"className":3293,"style":379},[96],[26,3295,3297,3300,3303,3306,3309,3312,3315],{"className":3296},[79],[26,3298],{"className":3299,"style":245},[83],[26,3301,295],{"className":3302},[88],[26,3304],{"className":3305,"style":1510},[96],[26,3307],{"className":3308,"style":97},[96],[26,3310,1429],{"className":3311},[101],[26,3313],{"className":3314,"style":1510},[96],[26,3316],{"className":3317,"style":97},[96],[26,3319,3321,3324,3327,3330,3333],{"className":3320},[79],[26,3322],{"className":3323,"style":245},[83],[26,3325,350],{"className":3326},[88],[26,3328],{"className":3329,"style":379},[96],[26,3331,353],{"className":3332},[383],[26,3334],{"className":3335,"style":379},[96],[26,3337,3339,3342,3345,3348,3351],{"className":3338},[79],[26,3340],{"className":3341,"style":84},[83],[26,3343,55],{"className":3344},[88,89],[26,3346],{"className":3347,"style":97},[96],[26,3349,59],{"className":3350},[101],[26,3352],{"className":3353,"style":97},[96],[26,3355,3357,3360],{"className":3356},[79],[26,3358],{"className":3359,"style":245},[83],[26,3361,2844],{"className":3362},[88],[10,3364,3365,3366,3368],{},"Нуль, помножений на будь-яке число, не дорівнює 6. ",[21,3367,3144],{}," коренів немає.",[14,3370,3372],{"id":3371},"задача-складаємо-рівняння","Задача: складаємо рівняння",[3374,3375,3376],"blockquote",{},[10,3377,3378],{},"Сума трьох послідовних натуральних чисел дорівнює 48. Знайдіть ці числа.",[10,3380,3381,3382,3410,3411,179,3463,456],{},"Нехай менше число ",[26,3383,3385,3398],{"className":3384},[33],[26,3386,3388],{"className":3387},[37],[39,3389,3390],{"xmlns":41},[44,3391,3392,3396],{},[47,3393,3394],{},[50,3395,55],{},[68,3397,55],{"encoding":70},[26,3399,3401],{"className":3400,"ariaHidden":65},[75],[26,3402,3404,3407],{"className":3403},[79],[26,3405],{"className":3406,"style":84},[83],[26,3408,55],{"className":3409},[88,89],", тоді наступні — ",[26,3412,3414,3432],{"className":3413},[33],[26,3415,3417],{"className":3416},[37],[39,3418,3419],{"xmlns":41},[44,3420,3421,3429],{},[47,3422,3423,3425,3427],{},[50,3424,55],{},[57,3426,1421],{},[223,3428,3201],{},[68,3430,3431],{"encoding":70},"x + 1",[26,3433,3435,3454],{"className":3434,"ariaHidden":65},[75],[26,3436,3438,3442,3445,3448,3451],{"className":3437},[79],[26,3439],{"className":3440,"style":3441},[83],"height:0.6667em;vertical-align:-0.0833em;",[26,3443,55],{"className":3444},[88,89],[26,3446],{"className":3447,"style":379},[96],[26,3449,1421],{"className":3450},[383],[26,3452],{"className":3453,"style":379},[96],[26,3455,3457,3460],{"className":3456},[79],[26,3458],{"className":3459,"style":245},[83],[26,3461,3201],{"className":3462},[88],[26,3464,3466,3484],{"className":3465},[33],[26,3467,3469],{"className":3468},[37],[39,3470,3471],{"xmlns":41},[44,3472,3473,3481],{},[47,3474,3475,3477,3479],{},[50,3476,55],{},[57,3478,1421],{},[223,3480,288],{},[68,3482,3483],{"encoding":70},"x + 2",[26,3485,3487,3505],{"className":3486,"ariaHidden":65},[75],[26,3488,3490,3493,3496,3499,3502],{"className":3489},[79],[26,3491],{"className":3492,"style":3441},[83],[26,3494,55],{"className":3495},[88,89],[26,3497],{"className":3498,"style":379},[96],[26,3500,1421],{"className":3501},[383],[26,3503],{"className":3504,"style":379},[96],[26,3506,3508,3511],{"className":3507},[79],[26,3509],{"className":3510,"style":245},[83],[26,3512,288],{"className":3513},[88],[26,3515,3517],{"className":3516},[29],[26,3518,3520,3593],{"className":3519},[33],[26,3521,3523],{"className":3522},[37],[39,3524,3525],{"xmlns":41,"display":42},[44,3526,3527,3590],{},[47,3528,3529,3531,3533,3535,3537,3539,3541,3543,3545,3547,3549,3551,3553,3555,3557,3560,3562,3564,3566,3568,3570,3572,3574,3576,3578,3580,3582,3584,3586,3588],{},[50,3530,55],{},[57,3532,1421],{},[57,3534,1721],{"stretchy":1720},[50,3536,55],{},[57,3538,1421],{},[223,3540,3201],{},[57,3542,1730],{"stretchy":1720},[57,3544,1421],{},[57,3546,1721],{"stretchy":1720},[50,3548,55],{},[57,3550,1421],{},[223,3552,288],{},[57,3554,1730],{"stretchy":1720},[57,3556,59],{},[223,3558,3559],{},"48",[96,3561],{"width":1426},[57,3563,1429],{},[96,3565],{"width":1426},[223,3567,225],{},[50,3569,55],{},[57,3571,1421],{},[223,3573,225],{},[57,3575,59],{},[223,3577,3559],{},[96,3579],{"width":1426},[57,3581,1429],{},[96,3583],{"width":1426},[50,3585,55],{},[57,3587,59],{},[223,3589,1440],{},[68,3591,3592],{"encoding":70},"x + (x + 1) + (x + 2) = 48 \\quad\\Rightarrow\\quad 3x + 3 = 48 \\quad\\Rightarrow\\quad x = 15",[26,3594,3596,3614,3635,3656,3677,3698,3722,3743,3761,3785,3803],{"className":3595,"ariaHidden":65},[75],[26,3597,3599,3602,3605,3608,3611],{"className":3598},[79],[26,3600],{"className":3601,"style":3441},[83],[26,3603,55],{"className":3604},[88,89],[26,3606],{"className":3607,"style":379},[96],[26,3609,1421],{"className":3610},[383],[26,3612],{"className":3613,"style":379},[96],[26,3615,3617,3620,3623,3626,3629,3632],{"className":3616},[79],[26,3618],{"className":3619,"style":1754},[83],[26,3621,1721],{"className":3622},[642],[26,3624,55],{"className":3625},[88,89],[26,3627],{"className":3628,"style":379},[96],[26,3630,1421],{"className":3631},[383],[26,3633],{"className":3634,"style":379},[96],[26,3636,3638,3641,3644,3647,3650,3653],{"className":3637},[79],[26,3639],{"className":3640,"style":1754},[83],[26,3642,3201],{"className":3643},[88],[26,3645,1730],{"className":3646},[715],[26,3648],{"className":3649,"style":379},[96],[26,3651,1421],{"className":3652},[383],[26,3654],{"className":3655,"style":379},[96],[26,3657,3659,3662,3665,3668,3671,3674],{"className":3658},[79],[26,3660],{"className":3661,"style":1754},[83],[26,3663,1721],{"className":3664},[642],[26,3666,55],{"className":3667},[88,89],[26,3669],{"className":3670,"style":379},[96],[26,3672,1421],{"className":3673},[383],[26,3675],{"className":3676,"style":379},[96],[26,3678,3680,3683,3686,3689,3692,3695],{"className":3679},[79],[26,3681],{"className":3682,"style":1754},[83],[26,3684,288],{"className":3685},[88],[26,3687,1730],{"className":3688},[715],[26,3690],{"className":3691,"style":97},[96],[26,3693,59],{"className":3694},[101],[26,3696],{"className":3697,"style":97},[96],[26,3699,3701,3704,3707,3710,3713,3716,3719],{"className":3700},[79],[26,3702],{"className":3703,"style":245},[83],[26,3705,3559],{"className":3706},[88],[26,3708],{"className":3709,"style":1510},[96],[26,3711],{"className":3712,"style":97},[96],[26,3714,1429],{"className":3715},[101],[26,3717],{"className":3718,"style":1510},[96],[26,3720],{"className":3721,"style":97},[96],[26,3723,3725,3728,3731,3734,3737,3740],{"className":3724},[79],[26,3726],{"className":3727,"style":308},[83],[26,3729,225],{"className":3730},[88],[26,3732,55],{"className":3733},[88,89],[26,3735],{"className":3736,"style":379},[96],[26,3738,1421],{"className":3739},[383],[26,3741],{"className":3742,"style":379},[96],[26,3744,3746,3749,3752,3755,3758],{"className":3745},[79],[26,3747],{"className":3748,"style":245},[83],[26,3750,225],{"className":3751},[88],[26,3753],{"className":3754,"style":97},[96],[26,3756,59],{"className":3757},[101],[26,3759],{"className":3760,"style":97},[96],[26,3762,3764,3767,3770,3773,3776,3779,3782],{"className":3763},[79],[26,3765],{"className":3766,"style":245},[83],[26,3768,3559],{"className":3769},[88],[26,3771],{"className":3772,"style":1510},[96],[26,3774],{"className":3775,"style":97},[96],[26,3777,1429],{"className":3778},[101],[26,3780],{"className":3781,"style":1510},[96],[26,3783],{"className":3784,"style":97},[96],[26,3786,3788,3791,3794,3797,3800],{"className":3787},[79],[26,3789],{"className":3790,"style":84},[83],[26,3792,55],{"className":3793},[88,89],[26,3795],{"className":3796,"style":97},[96],[26,3798,59],{"className":3799},[101],[26,3801],{"className":3802,"style":97},[96],[26,3804,3806,3809],{"className":3805},[79],[26,3807],{"className":3808,"style":245},[83],[26,3810,1440],{"className":3811},[88],[10,3813,3814,3816],{},[21,3815,3144],{}," 15, 16, 17.",[14,3818,3820],{"id":3819},"типові-помилки-семикласників","Типові помилки семикласників",[3822,3823,3824,3979,4158],"ul",{},[1217,3825,3826,3827,3830,3831,3905,3906,414],{},"Переносять доданок, ",[21,3828,3829],{},"не змінивши знак",": з ",[26,3832,3834,3857],{"className":3833},[33],[26,3835,3837],{"className":3836},[37],[39,3838,3839],{"xmlns":41},[44,3840,3841,3854],{},[47,3842,3843,3845,3847,3849,3851],{},[50,3844,55],{},[57,3846,1421],{},[223,3848,295],{},[57,3850,59],{},[223,3852,3853],{},"9",[68,3855,3856],{"encoding":70},"x + 5 = 9",[26,3858,3860,3878,3896],{"className":3859,"ariaHidden":65},[75],[26,3861,3863,3866,3869,3872,3875],{"className":3862},[79],[26,3864],{"className":3865,"style":3441},[83],[26,3867,55],{"className":3868},[88,89],[26,3870],{"className":3871,"style":379},[96],[26,3873,1421],{"className":3874},[383],[26,3876],{"className":3877,"style":379},[96],[26,3879,3881,3884,3887,3890,3893],{"className":3880},[79],[26,3882],{"className":3883,"style":245},[83],[26,3885,295],{"className":3886},[88],[26,3888],{"className":3889,"style":97},[96],[26,3891,59],{"className":3892},[101],[26,3894],{"className":3895,"style":97},[96],[26,3897,3899,3902],{"className":3898},[79],[26,3900],{"className":3901,"style":245},[83],[26,3903,3853],{"className":3904},[88]," пишуть ",[26,3907,3909,3931],{"className":3908},[33],[26,3910,3912],{"className":3911},[37],[39,3913,3914],{"xmlns":41},[44,3915,3916,3928],{},[47,3917,3918,3920,3922,3924,3926],{},[50,3919,55],{},[57,3921,59],{},[223,3923,3853],{},[57,3925,1421],{},[223,3927,295],{},[68,3929,3930],{"encoding":70},"x = 9 + 5",[26,3932,3934,3952,3970],{"className":3933,"ariaHidden":65},[75],[26,3935,3937,3940,3943,3946,3949],{"className":3936},[79],[26,3938],{"className":3939,"style":84},[83],[26,3941,55],{"className":3942},[88,89],[26,3944],{"className":3945,"style":97},[96],[26,3947,59],{"className":3948},[101],[26,3950],{"className":3951,"style":97},[96],[26,3953,3955,3958,3961,3964,3967],{"className":3954},[79],[26,3956],{"className":3957,"style":308},[83],[26,3959,3853],{"className":3960},[88],[26,3962],{"className":3963,"style":379},[96],[26,3965,1421],{"className":3966},[383],[26,3968],{"className":3969,"style":379},[96],[26,3971,3973,3976],{"className":3972},[79],[26,3974],{"className":3975,"style":245},[83],[26,3977,295],{"className":3978},[88],[1217,3980,3981,3982,4097,4098,4101,4102,414],{},"Розкриваючи дужки з мінусом, змінюють знак лише першого доданка: ",[26,3983,3985,4019],{"className":3984},[33],[26,3986,3988],{"className":3987},[37],[39,3989,3990],{"xmlns":41},[44,3991,3992,4016],{},[47,3993,3994,3996,3998,4000,4002,4004,4006,4008,4010,4012,4014],{},[57,3995,285],{},[57,3997,1721],{"stretchy":1720},[50,3999,55],{},[57,4001,285],{},[223,4003,225],{},[57,4005,1730],{"stretchy":1720},[57,4007,59],{},[57,4009,285],{},[50,4011,55],{},[57,4013,285],{},[223,4015,225],{},[68,4017,4018],{"encoding":70},"-(x - 3) = -x - 3",[26,4020,4022,4046,4067,4088],{"className":4021,"ariaHidden":65},[75],[26,4023,4025,4028,4031,4034,4037,4040,4043],{"className":4024},[79],[26,4026],{"className":4027,"style":1754},[83],[26,4029,285],{"className":4030},[88],[26,4032,1721],{"className":4033},[642],[26,4035,55],{"className":4036},[88,89],[26,4038],{"className":4039,"style":379},[96],[26,4041,285],{"className":4042},[383],[26,4044],{"className":4045,"style":379},[96],[26,4047,4049,4052,4055,4058,4061,4064],{"className":4048},[79],[26,4050],{"className":4051,"style":1754},[83],[26,4053,225],{"className":4054},[88],[26,4056,1730],{"className":4057},[715],[26,4059],{"className":4060,"style":97},[96],[26,4062,59],{"className":4063},[101],[26,4065],{"className":4066,"style":97},[96],[26,4068,4070,4073,4076,4079,4082,4085],{"className":4069},[79],[26,4071],{"className":4072,"style":3441},[83],[26,4074,285],{"className":4075},[88],[26,4077,55],{"className":4078},[88,89],[26,4080],{"className":4081,"style":379},[96],[26,4083,285],{"className":4084},[383],[26,4086],{"className":4087,"style":379},[96],[26,4089,4091,4094],{"className":4090},[79],[26,4092],{"className":4093,"style":245},[83],[26,4095,225],{"className":4096},[88]," — ",[21,4099,4100],{},"неправильно",", має бути ",[26,4103,4105,4125],{"className":4104},[33],[26,4106,4108],{"className":4107},[37],[39,4109,4110],{"xmlns":41},[44,4111,4112,4122],{},[47,4113,4114,4116,4118,4120],{},[57,4115,285],{},[50,4117,55],{},[57,4119,1421],{},[223,4121,225],{},[68,4123,4124],{"encoding":70},"-x + 3",[26,4126,4128,4149],{"className":4127,"ariaHidden":65},[75],[26,4129,4131,4134,4137,4140,4143,4146],{"className":4130},[79],[26,4132],{"className":4133,"style":3441},[83],[26,4135,285],{"className":4136},[88],[26,4138,55],{"className":4139},[88,89],[26,4141],{"className":4142,"style":379},[96],[26,4144,1421],{"className":4145},[383],[26,4147],{"className":4148,"style":379},[96],[26,4150,4152,4155],{"className":4151},[79],[26,4153],{"className":4154,"style":245},[83],[26,4156,225],{"className":4157},[88],[1217,4159,4160,4161,4222,4223,4274,4275,414],{},"Ділять на коефіцієнт, не дивлячись на знак: з ",[26,4162,4164,4186],{"className":4163},[33],[26,4165,4167],{"className":4166},[37],[39,4168,4169],{"xmlns":41},[44,4170,4171,4183],{},[47,4172,4173,4175,4177,4179,4181],{},[57,4174,285],{},[223,4176,288],{},[50,4178,55],{},[57,4180,59],{},[223,4182,1303],{},[68,4184,4185],{"encoding":70},"-2x = 8",[26,4187,4189,4213],{"className":4188,"ariaHidden":65},[75],[26,4190,4192,4195,4198,4201,4204,4207,4210],{"className":4191},[79],[26,4193],{"className":4194,"style":308},[83],[26,4196,285],{"className":4197},[88],[26,4199,288],{"className":4200},[88],[26,4202,55],{"className":4203},[88,89],[26,4205],{"className":4206,"style":97},[96],[26,4208,59],{"className":4209},[101],[26,4211],{"className":4212,"style":97},[96],[26,4214,4216,4219],{"className":4215},[79],[26,4217],{"className":4218,"style":245},[83],[26,4220,1303],{"className":4221},[88]," отримують ",[26,4224,4226,4244],{"className":4225},[33],[26,4227,4229],{"className":4228},[37],[39,4230,4231],{"xmlns":41},[44,4232,4233,4241],{},[47,4234,4235,4237,4239],{},[50,4236,55],{},[57,4238,59],{},[223,4240,2396],{},[68,4242,4243],{"encoding":70},"x = 4",[26,4245,4247,4265],{"className":4246,"ariaHidden":65},[75],[26,4248,4250,4253,4256,4259,4262],{"className":4249},[79],[26,4251],{"className":4252,"style":84},[83],[26,4254,55],{"className":4255},[88,89],[26,4257],{"className":4258,"style":97},[96],[26,4260,59],{"className":4261},[101],[26,4263],{"className":4264,"style":97},[96],[26,4266,4268,4271],{"className":4267},[79],[26,4269],{"className":4270,"style":245},[83],[26,4272,2396],{"className":4273},[88]," замість ",[26,4276,4278,4298],{"className":4277},[33],[26,4279,4281],{"className":4280},[37],[39,4282,4283],{"xmlns":41},[44,4284,4285,4295],{},[47,4286,4287,4289,4291,4293],{},[50,4288,55],{},[57,4290,59],{},[57,4292,285],{},[223,4294,2396],{},[68,4296,4297],{"encoding":70},"x = -4",[26,4299,4301,4319],{"className":4300,"ariaHidden":65},[75],[26,4302,4304,4307,4310,4313,4316],{"className":4303},[79],[26,4305],{"className":4306,"style":84},[83],[26,4308,55],{"className":4309},[88,89],[26,4311],{"className":4312,"style":97},[96],[26,4314,59],{"className":4315},[101],[26,4317],{"className":4318,"style":97},[96],[26,4320,4322,4325,4328],{"className":4321},[79],[26,4323],{"className":4324,"style":308},[83],[26,4326,285],{"className":4327},[88],[26,4329,2396],{"className":4330},[88],[14,4332,4334],{"id":4333},"спробуйте-самі","Спробуйте самі",[10,4336,4337,4338,414],{},"Розв’яжіть рівняння ",[26,4339,4341,4377],{"className":4340},[33],[26,4342,4344],{"className":4343},[37],[39,4345,4346],{"xmlns":41},[44,4347,4348,4374],{},[47,4349,4350,4352,4354,4356,4358,4360,4362,4364,4366,4368,4370,4372],{},[223,4351,360],{},[57,4353,285],{},[223,4355,288],{},[57,4357,1721],{"stretchy":1720},[50,4359,55],{},[57,4361,285],{},[223,4363,3201],{},[57,4365,1730],{"stretchy":1720},[57,4367,59],{},[50,4369,55],{},[57,4371,285],{},[223,4373,225],{},[68,4375,4376],{"encoding":70},"7 - 2(x - 1) = x - 3",[26,4378,4380,4398,4422,4443,4461],{"className":4379,"ariaHidden":65},[75],[26,4381,4383,4386,4389,4392,4395],{"className":4382},[79],[26,4384],{"className":4385,"style":308},[83],[26,4387,360],{"className":4388},[88],[26,4390],{"className":4391,"style":379},[96],[26,4393,285],{"className":4394},[383],[26,4396],{"className":4397,"style":379},[96],[26,4399,4401,4404,4407,4410,4413,4416,4419],{"className":4400},[79],[26,4402],{"className":4403,"style":1754},[83],[26,4405,288],{"className":4406},[88],[26,4408,1721],{"className":4409},[642],[26,4411,55],{"className":4412},[88,89],[26,4414],{"className":4415,"style":379},[96],[26,4417,285],{"className":4418},[383],[26,4420],{"className":4421,"style":379},[96],[26,4423,4425,4428,4431,4434,4437,4440],{"className":4424},[79],[26,4426],{"className":4427,"style":1754},[83],[26,4429,3201],{"className":4430},[88],[26,4432,1730],{"className":4433},[715],[26,4435],{"className":4436,"style":97},[96],[26,4438,59],{"className":4439},[101],[26,4441],{"className":4442,"style":97},[96],[26,4444,4446,4449,4452,4455,4458],{"className":4445},[79],[26,4447],{"className":4448,"style":3441},[83],[26,4450,55],{"className":4451},[88,89],[26,4453],{"className":4454,"style":379},[96],[26,4456,285],{"className":4457},[383],[26,4459],{"className":4460,"style":379},[96],[26,4462,4464,4467],{"className":4463},[79],[26,4465],{"className":4466,"style":245},[83],[26,4468,225],{"className":4469},[88],[4471,4472,4473],"answer",{},[10,4474,4475,4783,4784,179,4879,414],{},[26,4476,4478,4546],{"className":4477},[33],[26,4479,4481],{"className":4480},[37],[39,4482,4483],{"xmlns":41},[44,4484,4485,4543],{},[47,4486,4487,4489,4491,4493,4495,4497,4499,4501,4503,4505,4507,4509,4511,4513,4515,4517,4519,4521,4523,4525,4527,4529,4531,4533,4535,4537,4539,4541],{},[223,4488,360],{},[57,4490,285],{},[223,4492,288],{},[50,4494,55],{},[57,4496,1421],{},[223,4498,288],{},[57,4500,59],{},[50,4502,55],{},[57,4504,285],{},[223,4506,225],{},[57,4508,1429],{},[223,4510,3853],{},[57,4512,285],{},[223,4514,288],{},[50,4516,55],{},[57,4518,59],{},[50,4520,55],{},[57,4522,285],{},[223,4524,225],{},[57,4526,1429],{},[223,4528,232],{},[57,4530,59],{},[223,4532,225],{},[50,4534,55],{},[57,4536,1429],{},[50,4538,55],{},[57,4540,59],{},[223,4542,2396],{},[68,4544,4545],{"encoding":70},"7 - 2x + 2 = x - 3 \\Rightarrow 9 - 2x = x - 3 \\Rightarrow 12 = 3x \\Rightarrow x = 4",[26,4547,4549,4567,4588,4606,4624,4642,4660,4681,4699,4717,4735,4756,4774],{"className":4548,"ariaHidden":65},[75],[26,4550,4552,4555,4558,4561,4564],{"className":4551},[79],[26,4553],{"className":4554,"style":308},[83],[26,4556,360],{"className":4557},[88],[26,4559],{"className":4560,"style":379},[96],[26,4562,285],{"className":4563},[383],[26,4565],{"className":4566,"style":379},[96],[26,4568,4570,4573,4576,4579,4582,4585],{"className":4569},[79],[26,4571],{"className":4572,"style":308},[83],[26,4574,288],{"className":4575},[88],[26,4577,55],{"className":4578},[88,89],[26,4580],{"className":4581,"style":379},[96],[26,4583,1421],{"className":4584},[383],[26,4586],{"className":4587,"style":379},[96],[26,4589,4591,4594,4597,4600,4603],{"className":4590},[79],[26,4592],{"className":4593,"style":245},[83],[26,4595,288],{"className":4596},[88],[26,4598],{"className":4599,"style":97},[96],[26,4601,59],{"className":4602},[101],[26,4604],{"className":4605,"style":97},[96],[26,4607,4609,4612,4615,4618,4621],{"className":4608},[79],[26,4610],{"className":4611,"style":3441},[83],[26,4613,55],{"className":4614},[88,89],[26,4616],{"className":4617,"style":379},[96],[26,4619,285],{"className":4620},[383],[26,4622],{"className":4623,"style":379},[96],[26,4625,4627,4630,4633,4636,4639],{"className":4626},[79],[26,4628],{"className":4629,"style":245},[83],[26,4631,225],{"className":4632},[88],[26,4634],{"className":4635,"style":97},[96],[26,4637,1429],{"className":4638},[101],[26,4640],{"className":4641,"style":97},[96],[26,4643,4645,4648,4651,4654,4657],{"className":4644},[79],[26,4646],{"className":4647,"style":308},[83],[26,4649,3853],{"className":4650},[88],[26,4652],{"className":4653,"style":379},[96],[26,4655,285],{"className":4656},[383],[26,4658],{"className":4659,"style":379},[96],[26,4661,4663,4666,4669,4672,4675,4678],{"className":4662},[79],[26,4664],{"className":4665,"style":245},[83],[26,4667,288],{"className":4668},[88],[26,4670,55],{"className":4671},[88,89],[26,4673],{"className":4674,"style":97},[96],[26,4676,59],{"className":4677},[101],[26,4679],{"className":4680,"style":97},[96],[26,4682,4684,4687,4690,4693,4696],{"className":4683},[79],[26,4685],{"className":4686,"style":3441},[83],[26,4688,55],{"className":4689},[88,89],[26,4691],{"className":4692,"style":379},[96],[26,4694,285],{"className":4695},[383],[26,4697],{"className":4698,"style":379},[96],[26,4700,4702,4705,4708,4711,4714],{"className":4701},[79],[26,4703],{"className":4704,"style":245},[83],[26,4706,225],{"className":4707},[88],[26,4709],{"className":4710,"style":97},[96],[26,4712,1429],{"className":4713},[101],[26,4715],{"className":4716,"style":97},[96],[26,4718,4720,4723,4726,4729,4732],{"className":4719},[79],[26,4721],{"className":4722,"style":245},[83],[26,4724,232],{"className":4725},[88],[26,4727],{"className":4728,"style":97},[96],[26,4730,59],{"className":4731},[101],[26,4733],{"className":4734,"style":97},[96],[26,4736,4738,4741,4744,4747,4750,4753],{"className":4737},[79],[26,4739],{"className":4740,"style":245},[83],[26,4742,225],{"className":4743},[88],[26,4745,55],{"className":4746},[88,89],[26,4748],{"className":4749,"style":97},[96],[26,4751,1429],{"className":4752},[101],[26,4754],{"className":4755,"style":97},[96],[26,4757,4759,4762,4765,4768,4771],{"className":4758},[79],[26,4760],{"className":4761,"style":84},[83],[26,4763,55],{"className":4764},[88,89],[26,4766],{"className":4767,"style":97},[96],[26,4769,59],{"className":4770},[101],[26,4772],{"className":4773,"style":97},[96],[26,4775,4777,4780],{"className":4776},[79],[26,4778],{"className":4779,"style":245},[83],[26,4781,2396],{"className":4782},[88],".\nПеревірка: ",[26,4785,4787,4813],{"className":4786},[33],[26,4788,4790],{"className":4789},[37],[39,4791,4792],{"xmlns":41},[44,4793,4794,4810],{},[47,4795,4796,4798,4800,4802,4804,4806,4808],{},[223,4797,360],{},[57,4799,285],{},[223,4801,288],{},[57,4803,353],{},[223,4805,225],{},[57,4807,59],{},[223,4809,3201],{},[68,4811,4812],{"encoding":70},"7 - 2 \\cdot 3 = 1",[26,4814,4816,4834,4852,4870],{"className":4815,"ariaHidden":65},[75],[26,4817,4819,4822,4825,4828,4831],{"className":4818},[79],[26,4820],{"className":4821,"style":308},[83],[26,4823,360],{"className":4824},[88],[26,4826],{"className":4827,"style":379},[96],[26,4829,285],{"className":4830},[383],[26,4832],{"className":4833,"style":379},[96],[26,4835,4837,4840,4843,4846,4849],{"className":4836},[79],[26,4838],{"className":4839,"style":245},[83],[26,4841,288],{"className":4842},[88],[26,4844],{"className":4845,"style":379},[96],[26,4847,353],{"className":4848},[383],[26,4850],{"className":4851,"style":379},[96],[26,4853,4855,4858,4861,4864,4867],{"className":4854},[79],[26,4856],{"className":4857,"style":245},[83],[26,4859,225],{"className":4860},[88],[26,4862],{"className":4863,"style":97},[96],[26,4865,59],{"className":4866},[101],[26,4868],{"className":4869,"style":97},[96],[26,4871,4873,4876],{"className":4872},[79],[26,4874],{"className":4875,"style":245},[83],[26,4877,3201],{"className":4878},[88],[26,4880,4882,4904],{"className":4881},[33],[26,4883,4885],{"className":4884},[37],[39,4886,4887],{"xmlns":41},[44,4888,4889,4901],{},[47,4890,4891,4893,4895,4897,4899],{},[223,4892,2396],{},[57,4894,285],{},[223,4896,225],{},[57,4898,59],{},[223,4900,3201],{},[68,4902,4903],{"encoding":70},"4 - 3 = 1",[26,4905,4907,4925,4943],{"className":4906,"ariaHidden":65},[75],[26,4908,4910,4913,4916,4919,4922],{"className":4909},[79],[26,4911],{"className":4912,"style":308},[83],[26,4914,2396],{"className":4915},[88],[26,4917],{"className":4918,"style":379},[96],[26,4920,285],{"className":4921},[383],[26,4923],{"className":4924,"style":379},[96],[26,4926,4928,4931,4934,4937,4940],{"className":4927},[79],[26,4929],{"className":4930,"style":245},[83],[26,4932,225],{"className":4933},[88],[26,4935],{"className":4936,"style":97},[96],[26,4938,59],{"className":4939},[101],[26,4941],{"className":4942,"style":97},[96],[26,4944,4946,4949],{"className":4945},[79],[26,4947],{"className":4948,"style":245},[83],[26,4950,3201],{"className":4951},[88],{"title":4953,"searchDepth":4954,"depth":4955,"links":4956},"",2,3,[4957,4958,4959,4960,4961,4962,4963,4964,4965,4966,4967],{"id":16,"depth":4954,"text":17},{"id":423,"depth":4954,"text":424},{"id":1151,"depth":4954,"text":1152},{"id":1274,"depth":4954,"text":1275},{"id":1699,"depth":4954,"text":1700},{"id":2365,"depth":4954,"text":2366},{"id":2805,"depth":4954,"text":2806},{"id":3176,"depth":4954,"text":3177},{"id":3371,"depth":4954,"text":3372},{"id":3819,"depth":4954,"text":3820},{"id":4333,"depth":4954,"text":4334},"2026-10-16","Що таке лінійне рівняння, як його розв’язувати і коли коренів немає або їх безліч. Пояснення теми з алгебри 7 класу з розв’язаними прикладами та задачею.",false,"md",null,{},true,"\u002Fblog\u002Fliniyni-rivnyannya-7-klas","---\ntitle: 'Лінійні рівняння з однією змінною, 7 клас: пояснення з прикладами'\ndescription: 'Що таке лінійне рівняння, як його розв’язувати і коли коренів немає або їх безліч. Пояснення теми з алгебри 7 класу з розв’язаними прикладами та задачею.'\ndate: '2026-10-16'\nsubject: math\ngrade: 7\ntopic: 'Лінійні рівняння'\ntags: [алгебра, 7 клас, лінійні рівняння, рівняння]\n---\n\nЛінійні рівняння — фундамент усієї шкільної алгебри. Якщо добре зрозуміти цю тему в 7 класі, то квадратні рівняння, системи й нерівності далі підуть набагато легше.\n\n## Що таке лінійне рівняння\n\n**Лінійним рівнянням з однією змінною** називають рівняння виду\n\n$$\nax = b,\n$$\n\nде $x$ — змінна, а $a$ і $b$ — числа. Наприклад: $3x = 12$, $-2x = 5$, $0 \\cdot x = 7$.\n\n**Корінь рівняння** — це значення змінної, при якому рівняння перетворюється на правильну числову рівність. Розв’язати рівняння — означає знайти всі його корені або довести, що їх немає.\n\n## Скільки коренів може бути\n\nУсе залежить від коефіцієнта $a$:\n\n| Випадок | Що отримуємо | Коренів |\n|---|---|---|\n| $a \\ne 0$ | $x = \\dfrac{b}{a}$ | один |\n| $a = 0$, $b = 0$ | $0 \\cdot x = 0$ — правильно для будь-якого $x$ | безліч |\n| $a = 0$, $b \\ne 0$ | $0 \\cdot x = b$ — неможливо | немає |\n\n## Два головні правила\n\nЩоб звести будь-яке рівняння до вигляду $ax = b$, користуємося двома властивостями:\n\n1. **Будь-який доданок можна перенести з однієї частини рівняння в іншу, змінивши його знак.**\n2. **Обидві частини рівняння можна помножити або поділити на одне й те саме число, яке не дорівнює нулю.**\n\nАлгоритм розв’язування:\n\n1. Розкрити дужки.\n2. Перенести доданки зі змінною вліво, числа — вправо.\n3. Звести подібні доданки.\n4. Поділити обидві частини на коефіцієнт при $x$.\n\n## Приклад 1. Найпростіший\n\n$$\n3x - 7 = 8\n$$\n\nПереносимо $-7$ вправо зі зміною знака:\n\n$$\n3x = 8 + 7 \\quad\\Rightarrow\\quad 3x = 15 \\quad\\Rightarrow\\quad x = 5\n$$\n\n**Перевірка:** $3 \\cdot 5 - 7 = 8$. ✓\n\n## Приклад 2. З дужками\n\n$$\n5(x - 2) = 2x + 11\n$$\n\nРозкриваємо дужки і переносимо:\n\n$$\n5x - 10 = 2x + 11 \\quad\\Rightarrow\\quad 5x - 2x = 11 + 10 \\quad\\Rightarrow\\quad 3x = 21 \\quad\\Rightarrow\\quad x = 7\n$$\n\n**Перевірка:** $5 \\cdot (7 - 2) = 25$ і $2 \\cdot 7 + 11 = 25$. ✓\n\n## Приклад 3. З дробами\n\n$$\n\\frac{x}{3} + \\frac{x}{4} = 7\n$$\n\nПозбуваємося знаменників: множимо обидві частини на спільний знаменник $12$:\n\n$$\n4x + 3x = 84 \\quad\\Rightarrow\\quad 7x = 84 \\quad\\Rightarrow\\quad x = 12\n$$\n\n## Приклад 4. Коренів безліч\n\n$$\n2(x + 3) = 2x + 6 \\quad\\Rightarrow\\quad 2x + 6 = 2x + 6 \\quad\\Rightarrow\\quad 0 \\cdot x = 0\n$$\n\nРівність правильна при будь-якому $x$. **Відповідь:** $x$ — будь-яке число.\n\n## Приклад 5. Коренів немає\n\n$$\n4x - 1 = 4x + 5 \\quad\\Rightarrow\\quad 0 \\cdot x = 6\n$$\n\nНуль, помножений на будь-яке число, не дорівнює 6. **Відповідь:** коренів немає.\n\n## Задача: складаємо рівняння\n\n> Сума трьох послідовних натуральних чисел дорівнює 48. Знайдіть ці числа.\n\nНехай менше число $x$, тоді наступні — $x + 1$ і $x + 2$:\n\n$$\nx + (x + 1) + (x + 2) = 48 \\quad\\Rightarrow\\quad 3x + 3 = 48 \\quad\\Rightarrow\\quad x = 15\n$$\n\n**Відповідь:** 15, 16, 17.\n\n## Типові помилки семикласників\n\n- Переносять доданок, **не змінивши знак**: з $x + 5 = 9$ пишуть $x = 9 + 5$.\n- Розкриваючи дужки з мінусом, змінюють знак лише першого доданка: $-(x - 3) = -x - 3$ — **неправильно**, має бути $-x + 3$.\n- Ділять на коефіцієнт, не дивлячись на знак: з $-2x = 8$ отримують $x = 4$ замість $x = -4$.\n\n## Спробуйте самі\n\nРозв’яжіть рівняння $7 - 2(x - 1) = x - 3$.\n\n::answer\n$7 - 2x + 2 = x - 3 \\Rightarrow 9 - 2x = x - 3 \\Rightarrow 12 = 3x \\Rightarrow x = 4$.\nПеревірка: $7 - 2 \\cdot 3 = 1$ і $4 - 3 = 1$.\n::\n",{"title":5,"description":4969},"blog\u002Fliniyni-rivnyannya-7-klas",[4980,4981,4982,4983],"алгебра","7 клас","лінійні рівняння","рівняння","Лінійні рівняння","olPVhtoYgrb88Gbo0Nv-sdyyuoZ3DDWdp4idZCD1AT4",[4987],{"path":4988,"title":4989,"date":4990},"\u002Fblog\u002Fkvadratni-rivnyannya-dyskryminant","Квадратні рівняння, 8 клас: пояснення через дискримінант і приклади","2026-10-10",1792103491838]