Решебник по алгебре 9 класс Мерзляк Задание 945

\[\boxed{\mathbf{945\ (945).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ (2x - 3)^{2} \leq\]

\[\leq (4x - 1)(x - 2) + 7\]

\[4x^{2} - 12x + 9 \leq 4x^{2} -\]

\[- 8x - x + 2 + 7\]

\[- 3x \leq 0\ \ \]

\[x \geq 0\]

\[Ответ:\lbrack 0;\ + \infty).\]

\[2)\ (x - 2)(2 + x) \geq 2 -\]

\[- (x + 4)(1 - x)\]

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

\[- 2 \geq 3x\ \ \]

\[x \leq - \frac{2}{3}\]

\[Ответ:\left( - \infty;\ - \frac{2}{3} \right\rbrack.\]

\[3)\ \frac{1 - x}{2} + 3 < 3x -\]

\[- \frac{2x + 1}{4}\ \ \ \ | \cdot 4\]

\[2 - 2x + 12 < 12x - 2x - 1\]

\[- 12x < - 15\]

\[x > \frac{15}{12}\]

\[\ x > 1\frac{1}{4}\]

\[Ответ:\left( 1\frac{1}{4}; + \infty \right).\]

\[4)\ \frac{3x - 37}{2} - 9 > \frac{7 - 2x}{4} +\]

\[+ 2x\ \ \ \ | \cdot 4\]

\[6x - 74 - 36 > 7 - 2x + 8x\]

\[- 117 > 0\]

\[Ответ:\ \varnothing.\]

\[5)\ \frac{5x - 3}{5} \geq \frac{3x + 4}{3} - \frac{29}{15}\text{\ \ \ \ \ }\]

\[\ | \cdot 15\]

\[15x - 9 \geq 15x + 20 - 29,\]

\[\ \ 0 \geq 0\]

\[Ответ:( - \infty;\ + \infty).\]