Решебник по алгебре 9 класс Мерзляк Задание 154

\[\boxed{\text{154\ (154).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ |x + 5| + 2x = 7\]

\[\left\{ \begin{matrix} x + 5 = 7 - 2x \\ 7 - 2x \geq 0\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} 3x = 2 \\ x \leq 3,5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = \frac{2}{3}\text{\ \ \ } \\ x \leq 3,5 \\ \end{matrix} \right.\ \Longrightarrow \ x = \frac{2}{3}\]

\[\left\{ \begin{matrix} - x - 5 = 7 - 2x \\ x \leq 3,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} x = 12 \\ x \leq 3,5 \\ \end{matrix} \right.\ \Longrightarrow не\ удовлетворяет.\]

\[Ответ:x = \frac{2}{3}.\]

\[2)\ |3 - 2x| - x = 9\]

\[\left\{ \begin{matrix} 3 - 2x = 9 + x \\ 9 + x \geq 0\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} - 3x = 6 \\ x \geq - 9\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 2 \\ x \geq - 9 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = - 2\]

\[\left\{ \begin{matrix} - 3 + 2x = 9 + x \\ x \geq - 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 9 + 3 \\ x \geq - 9\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = 12 \\ x \geq - 9 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = 12\]

\[Ответ:\ x = - 2;x = 12.\]