Решебник по алгебре 9 класс Мерзляк Задание 192

\[\boxed{\text{192\ (192).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\left\{ \begin{matrix} 8(2 - x) - 2x > 3\ \ \ \ \ \\ - 3(6x - 1) - x < 2x \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} 16 - 8x - 2x > 3\ \ \ \\ - 18x + 3 - x < 2x \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 10x > - 13 \\ - 21x < - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x < \frac{13}{10} \\ x > \frac{1}{7}\text{\ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x < 1,3 \\ x > \frac{1}{7}\text{\ \ \ } \\ \end{matrix} \right.\ \]

\[Ответ:x \in \left( \frac{1}{7};1,3 \right).\]

\[2)\ \left\{ \begin{matrix} \frac{x + 1^{\backslash 3}}{4} - \frac{2x + 3^{\backslash 4}}{3} > 1\ \ \ \ \ \\ 6(2x - 1) < 5(x - 4) - 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} \frac{3x + 3 - 8x - 12}{12} > 1\ \ | \cdot 12 \\ 12x - 6 < 5x - 20 - 7\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 5x > 21 \\ 7x < - 21 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x < - \frac{21}{5} \\ x < - 3\ \ \\ \end{matrix} \right.\ \ \]

\[Ответ:x \in ( - \infty;\ - 4,2).\]

\[3)\ \left\{ \begin{matrix} 2(x - 3) \leq 3x + 4(x + 1)\text{\ \ \ \ \ \ \ \ } \\ (x - 3)(x + 3) \leq (x - 4)^{2} - 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2x - 6 \leq 3x + 4x + 4\ \ \ \ \ \ \ \ \ \ \\ x^{2} - 9 \leq x^{2} - 8x + 16 - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 5x \leq 10 \\ 8x \leq 24 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq - 2 \\ x \leq 3\ \ \\ \end{matrix} \right.\ \]

\[Ответ:x \in \lbrack - 2;3\rbrack.\]

\[4)\ \left\{ \begin{matrix} 2(x + 11) \geq 3(6 - x)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ (x - 3)(x + 6) \geq (x + 5)(x - 4) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 5x \geq - 4 \\ 2x \geq - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq - \frac{4}{5} \\ x \geq - 1 \\ \end{matrix} \right.\ \]

\[Ответ:x \in \lbrack - 0,8;\ + \infty).\]

\[\left\{ \begin{matrix} 7x \leq 5\ \ \ \ \ \\ 14x \geq 10 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \leq \frac{5}{7} \\ x \geq \frac{5}{7} \\ \end{matrix} \right.\ \]

\[Ответ:\left\{ \frac{5}{7} \right\}.\]