Основы алгебры Примеры

$3 x - 2 = 3 (x - \frac{2}{3})$

Этап 1

Упростим $3 (x - \frac{2}{3})$ .

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Этап 1.1

Применим свойство дистрибутивности.

$3 x - 2 = 3 x + 3 (- \frac{2}{3})$

Этап 1.2

Сократим общий множитель $3$ .

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Этап 1.2.1

Перенесем стоящий впереди знак минуса в $- \frac{2}{3}$ в числитель.

$3 x - 2 = 3 x + 3 (\frac{- 2}{3})$

Этап 1.2.2

Сократим общий множитель.

$3 x - 2 = 3 x + 3 (\frac{- 2}{3})$

Этап 1.2.3

Перепишем это выражение.

$3 x - 2 = 3 x - 2$

Этап 2

Построим график каждой части уравнения. Решение — абсцисса (координата x) точки пересечения.

$x \approx - 50, - 49.8, - 49.7, - 49.6, - 49.4, - 49.3, - 49.2, - 49, - 48.9, - 48.8, - 48.6, - 48.5, - 48.4, - 48.2, - 48.1, - 48, - 47.8, - 47.7, - 47.6, - 47.4, - 47.3, - 47.2, - 47.1, - 47, - 46.9, - 46.8, - 46.6, - 46.5, - 46.3\overline{9}, - 46.1\overline{9}, - 46.0\overline{9}, - 46, - 45.7\overline{9}, - 45.6\overline{9}, - 45.5\overline{9}, - 45.3\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 45, - 44.8\overline{9}, - 44.7\overline{9}, - 44.5\overline{9}, - 44.4\overline{9}, - 44.3\overline{9}, - 44.1\overline{9}, - 44.0\overline{9}, - 44, - 43.7\overline{9}, - 43.6\overline{9}, - 43.5\overline{9}, - 43.3\overline{9}, - 43.2\overline{9}, - 43.1\overline{9}, - 43, - 42.8\overline{9}, - 42.7\overline{9}, - 42.5\overline{9}, - 42.4\overline{9}, - 42.3\overline{9}, - 42.1\overline{9}, - 42.0\overline{9}, - 42, - 41.7\overline{9}, - 41.5\overline{9}, - 41.4\overline{9}, - 41.3\overline{9}, - 41.2\overline{9}, - 41.1\overline{9}, - 41, - 40.7\overline{9}, - 40.5\overline{9}, - 40.3\overline{9}, - 40.1\overline{9}, - 40, - 39.7\overline{9}, - 39.5\overline{9}, - 39.3\overline{9}, - 39.1\overline{9}, - 39, - 38.7\overline{9}, - 38.5\overline{9}, - 38.3\overline{9}, - 38.1\overline{9}, - 38, - 37.7\overline{9}, - 37.5\overline{9}, - 37.3\overline{9}, - 37.1\overline{9}, - 37, - 36.7\overline{9}, - 36.5\overline{9}, - 36.3\overline{9}, - 36.2\overline{9}, - 36.1\overline{9}, - 36.0\overline{9}, - 36, - 35.7\overline{9}, - 35.5\overline{9}, - 35.3\overline{9}, - 35.1\overline{9}, - 35, - 34.7\overline{9}, - 34.5\overline{9}, - 34.3\overline{9}, - 34.1\overline{9}, - 34, - 33.7\overline{9}, - 33.5\overline{9}, - 33.3\overline{9}, - 33.1\overline{9}, - 33, - 32.7\overline{9}, - 32.5\overline{9}, - 32.3\overline{9}, - 32.1\overline{9}, - 32, - 31.7\overline{9}, - 31.5\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 30.6\overline{9}, - 30.5\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 22, - 21.8\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 18.5\overline{9}, - 18.4\overline{9}, - 14.8\overline{9}, - 14.7\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - \frac{29}{2}, - 14.3\overline{9}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.6\overline{9}, - 13.5\overline{9}, - \frac{27}{2}, - 13.2\overline{9}, - 13.1\overline{9}, - 13.0\overline{9}, - 13, - 12.8\overline{9}, - 12.7\overline{9}, - 12.6\overline{9}, - \frac{25}{2}, - \frac{62}{5}, - 12.2\overline{9}, - 12.1\overline{9}, - 12.0\overline{9}, - 12, - 11.8\overline{9}, - 11.6\overline{9}, - \frac{58}{5}, - \frac{57}{5}, - 11.2\overline{9}, - \frac{56}{5}, - 11.0\overline{9}, - 10.8\overline{9}, - \frac{54}{5}, - 10.6\overline{9}, - \frac{53}{5}, - \frac{21}{2}, - \frac{52}{5}, - 10.2\overline{9}, - 10.0\overline{9}, - 10, - \frac{49}{5}, - 9.7, - \frac{48}{5}, - \frac{19}{2}, - \frac{47}{5}, - 9.3, - \frac{46}{5}, - 9, - \frac{44}{5}, - \frac{43}{5}, - \frac{42}{5}, - \frac{41}{5}, - 8, - \frac{39}{5}, - \frac{38}{5}, - \frac{37}{5}, - 7.3, - \frac{36}{5}, - 7, - 6.9, - \frac{33}{5}, - \frac{13}{2}, - \frac{31}{5}, - 6.1, - \frac{29}{5}, - 5.7, - \frac{27}{5}, - 5.3, - 5, - 4.9, - 3.9, - \frac{19}{5}, - 3.7, - \frac{7}{2}, - \frac{17}{5}, - \frac{16}{5}, - 3.1, - 3, - 2.9, - 2.7, - \frac{13}{5}, - \frac{12}{5}, - 2.3, - \frac{11}{5}, - 2.1, - 2, - 1.9, - 1.7, - \frac{8}{5}, - \frac{3}{2}, - 1.3, - \frac{6}{5}, - 1.1, - 1, - 0.7, - \frac{3}{5}, - \frac{1}{2}, - \frac{2}{5}, - 0.3, - \frac{1}{5}, 0, 0.1, 0.3, \frac{3}{5}, 0.7, 0.9, 1, \frac{6}{5}, 1.3, \frac{7}{5}, \frac{3}{2}, \frac{8}{5}, 1.7, \frac{9}{5}, 2, 2.1, \frac{11}{5}, \frac{12}{5}, \frac{5}{2}, \frac{13}{5}, \frac{14}{5}, 3, \frac{16}{5}, 3.3, \frac{17}{5}, \frac{7}{2}, \frac{18}{5}, \frac{19}{5}, 3.9, 5.7, \frac{29}{5}, 6.1, \frac{31}{5}, \frac{13}{2}, \frac{33}{5}, 6.9, 7, 7.3, \frac{37}{5}, 7.7, \frac{39}{5}, 8.1, \frac{41}{5}, \frac{17}{2}, \frac{43}{5}, 8.7, 8.9, 9.1, 9.3, \frac{47}{5}, 9.7, 9.9, 10.1, 10.3, \frac{52}{5}, 10.7, 10.9, 11.1, \frac{56}{5}, 11.3, \frac{57}{5}, 11.7, \frac{59}{5}, 11.9, 12, 12.2, 12.3, \frac{62}{5}, \frac{25}{2}, 12.6, 12.7, 12.8, 13, 13.1, 13.2, 13.3, 13.4, \frac{27}{2}, 13.6, 14, 14.1, 14.2, 14.3, 14.4, \frac{29}{2}, 14.6, 14.7, 14.8, 14.9, 15, 15.1, 15.2, 15.4, \frac{31}{2}, 15.6, 15.7, 15.8, 15.9, 16, 16.1, 16.2, 16.3, 16.4, \frac{33}{2}, 16.6, 16.8, 16.9, 17, 17.1, 17.2, 17.3, 17.4, \frac{35}{2}, 17.6, 17.7, 17.8, 17.9, 18, 18.1, 18.2, 18.3, 18.4, 18.5, 18.8, 18.9, 19, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.9, 20, 20.1, 20.2, 20.3, 20.4, 20.5, 20.6, 20.7, 20.8, 20.9, 21, 21.1, 21.2, 21.3, 21.6, 21.9, 22, 22.1, 22.4, 22.5, 23.2, 23.3, 23.6, 23.7, 24, 24.1, 24.4, 24.5, 25.2, 25.3, 26, 26.1, 26.4, 26.5, 26.8, 26.9, 27.2, 27.3, 28, 28.1, 28.4, 28.5, 28.8, 28.9, 29.2, 29.3, 29.6, 29.7, 30, 30.1, 30.8, 30.9, 31.2, 31.3, 31.6, 31.7, 32.7, 32.8, 33, 33.2, 33.4, 33.6, 33.8, 34, 34.2, 34.4, 34.6, 34.8, 35, 35.2, 35.4, 35.6, 35.8, 36, 36.2, 36.4, 36.6, 36.8, 37, 37.2, 37.4, 37.6, 37.8, 38, 38.2, 38.4, 38.6, 38.8, 39, 39.2, 39.4, 39.6, 39.8, 40, 40.2, 40.4, 40.6, 40.8, 41, 41.3, 41.4, 41.6, 41.8, 42, 42.2, 42.4, 42.6, 42.8, 43, 43.2, 43.4, 43.5, 43.6, 43.8, 43.9, 44, 44.2, 44.3, 44.4, 44.7, 44.8, 45, 45.1, 45.2, 45.4, 45.5, 45.6, 45.8, 45.9, 46, 46.2, 46.3, 46.4, 46.7, 46.8, 47, 47.1, 47.2, 47.4, 47.5, 47.6, 47.8, 47.9, 48, 48.2, 48.3, 48.4, 48.6, 48.7, 48.8, 49, 49.1, 49.2, 49.4, 49.5, 49.6, 49.8, 49.9$

Этап 3