Решебник по алгебре 9 класс Мерзляк Задание 153

\[\boxed{\text{153\ (153).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ |x - 3| + x = 15\]

\[|x - 3| = 15 - x\]

\[\left\{ \begin{matrix} x - 3 = 15 - x \\ 15 - x \geq 0\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x = 18 \\ x \leq 15\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 9\ \ \ \\ x \leq 15 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = 9\]

\[\left\{ \begin{matrix} - x + 3 = 15 - x \\ 15 - x \geq 0\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 0 \cdot x = - 12 \\ x \leq 15\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \ \ нет\ корней.\]

\[Ответ:x = 9.\]

\[2)\ |x + 1| - 4x = 14\]

\[\left\{ \begin{matrix} x + 1 = 4x + 14 \\ 4x + 14 \geq 0\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 3x = 13 \\ x \geq - 3,5\ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = - 4\frac{1}{3} \\ x \geq - 3,5 \\ \end{matrix} \right.\ \Longrightarrow \text{\ \ }\]

\[\Longrightarrow не\ удовлетворяет.\]

\[\left\{ \begin{matrix} - x - 1 = 4x + 14 \\ x \geq - 3,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 5x = 15 \\ x \geq - 3,5\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 3\ \ \ \ \\ x \geq - 3,5 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = - 3\]

\[Ответ:\ x = - 3.\ \]

\[3)\ |3x - 12| - 2x = 1\]

\[\left\{ \begin{matrix} 3x - 12 = 1 + 2x \\ 1 + 2x \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 13\ \ \ \ \\ x \geq - 0,5 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = 13\]

\[\left\{ \begin{matrix} - 3x + 12 = 1 + 2x \\ x \geq - 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 5x = - 11 \\ x \geq - 0,5\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = \frac{11}{5}\text{\ \ \ \ } \\ x \geq - 0,5 \\ \end{matrix} \right.\ \Longrightarrow \ \ x = 2,2\]

\[Ответ:x = 13;x = 2,2.\ \]

\[4)\ |x + 2| - x = 1\]

\[\left\{ \begin{matrix} x + 2 = 1 + x \\ 1 + x \geq 0\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 0 \cdot x = - 1 \\ x \geq - 1\ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \ \ нет\ корней\]

\[\left\{ \begin{matrix} - x - 2 = 1 + x \\ x \geq - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 2x = 3 \\ x \geq - 1\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 1,5 \\ x \geq - 1\ \ \ \\ \end{matrix}\ \right.\ \Longrightarrow\]

\[\Longrightarrow не\ удовлетворяет.\]

\[Ответ:нет\ корней.\]