Решебник по алгебре 9 класс Мерзляк Задание 108

\[\boxed{\text{108\ (108).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 9 - 7 \cdot (x + 3) = 5 - 6x\]

\[9 - 7x - 21 - 5 + 6x = 0\]

\[- x - 17 = 0\]

\[x = - 17\]

\[Ответ:\ - 17.\]

\[2)\ \frac{x + 3^{\backslash 7}}{2} - \frac{x - 4^{\backslash 2}}{7} = 1^{\backslash 14}\]

\[\frac{7x + 21 - 2x + 8 - 14}{14} = 0\]

\[5x + 15 = 0\]

\[5x = - 15\]

\[x = - 3\]

\[Ответ:\ - 3.\]

\[3)\ (x + 7)^{2} - (x - 2)^{2} = 15\]

\[x^{2} + 14x + 49 - x^{2} + 4x -\]

\[- 4 - 15 = 0\]

\[18x + 30 = 0\]

\[x = - \frac{30}{18}\]

\[x = - \frac{5}{3}\]

\[Ответ:\ - 1\frac{2}{3}.\]

\[4)\ 5x - 2 = 3(3x - 1) - 4x - 4\]

\[5x - 2 = 9x - 3 - 4x - 4\]

\[5x - 9x + 4x = 2 - 3 - 4\]

\[0 \cdot x = - 5\]

\[Ответ:нет\ корней.\]

\[5)\ 6x + (x - 2)(x + 2) =\]

\[= (x + 3)^{2} - 13\]

\[6x + x^{2} - 4 = x^{2} + 6x + 9 - 13\]

\[6x + x^{2} - x^{2} - 6x =\]

\[= 4 + 9 - 13\]

\[0x = 0\]

\[Ответ:x - любое\ число.\ \ \]

\[6)\ (x + 6)(x - 1) -\]

\[- (x + 3)(x - 4) = 5x\]

\[x^{2} - x + 6x - 6 - x^{2} + 4x -\]

\[- 3x + 12 - 5x = 0\]

\[x + 6 = 0\]

\[x = - 6\]

\[Ответ:\ - 6.\]