Решебник по алгебре 7 класс Мерзляк Задание 68

\[\boxed{\text{68\ (68).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ |x| + 3x = 12\]

\[x \geq 0;\ \ |x| = x:\]

\[x + 3x = 12\]

\[4x = 2\]

\[x = 3.\]

\[x < 0;\ \ |x| = - x:\]

\[- x + 3x = 12\]

\[2x = 12\]

\[x = 6 - не\ удовлетворяет.\]

\[Ответ:x = 3.\]

\[2)\ |x| - 4x = 9\]

\[x \geq 0;\ \ |x| = x:\]

\[x - 4x = 9\]

\(- 3x = 9\)

\[x = - 3 - не\ удовлетворяет.\]

\[x < 0;\ \ \ |x| = - x:\]

\[- x - 4x = 9\]

\[- 5x = 9\]

\[x = - 1,8.\]

\[Ответ:\ x = - 1,8.\]

\[3)\ 2 \cdot (x - 5) - 6 \cdot |x| = - 18\]

\[x \geq 0;\ \ |x| = x:\]

\[2x - 10 - 6x = - 18\]

\[- 4x = - 18 + 10\]

\[- 4x = - 8\]

\[x = 2.\]

\[x < 0;\ \ |x| = - x:\]

\[2x - 10 + 6x = - 18\]

\[8x = - 18 + 10\]

\[8x = - 8\]

\[x = - 1.\]

\[Ответ:\ x = - 1;2.\]