Решебник по алгебре 9 класс Мерзляк Задание 184

\[\boxed{\text{184\ (184).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\left\{ \begin{matrix} - 4x \leq - 12 \\ x + 2 > 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 3 \\ x > 4 \\ \end{matrix} \right.\ \]

\[Ответ:(4;\ + \infty).\]

\[2)\ \left\{ \begin{matrix} 8 - x \geq 5 \\ x - 7 \leq 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} - x \geq - 3 \\ x \leq 9\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x \leq 3 \\ x \leq 9 \\ \end{matrix} \right.\ \]

\[Ответ:( - \infty;3\rbrack.\]

\[3)\ \left\{ \begin{matrix} 3x - 3 < 5x\ \ \ \\ 7x - 10 < 5x \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} - 2x < 3 \\ 2x < 10 \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} x > - 1,5 \\ x < 5\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:( - 1,5;5).\]

\[4)\ \left\{ \begin{matrix} 2 - 3x < 4x - 12 \\ 7 + 3x \geq 2x + 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 7x < - 14 \\ x \geq 3\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x > 2 \\ x \geq 3 \\ \end{matrix} \right.\ \]

\[Ответ:\lbrack 3;\ + \infty).\]

\[5)\ \left\{ \begin{matrix} x + 3 \geq 8 \\ \frac{x + 1}{3} < 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 5\ \ \ \ \ \ \ \ \ \\ x + 1 < 18 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x \geq 5\ \ \ \\ x < 17 \\ \end{matrix} \right.\ \]

\[Ответ:\lbrack 5;17)\text{.\ }\]

\[6)\ \left\{ \begin{matrix} 5x - 2 \geq 2x + 1\ \ \\ 2x + 3 \leq 33 - 3x \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 3x \geq 3\ \ \\ 5x \leq 30 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 1 \\ x \leq 6 \\ \end{matrix} \right.\ \]

\[Ответ:\lbrack 1;6\rbrack.\]