Задача 9. Решите неравенство    \(-3\left( {x + 2} \right)-4 \geqslant 2-5\left( {2-2x} \right)\)

Ответ

ОТВЕТ: \(\left( {-\infty ;\;-\dfrac{2}{{13}}} \right].\)

Решение

\(-3\left( {x + 2} \right)-4 \ge 2-5\left( {2-2x} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,-3x-6-4 \ge 2-10 + 10x\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,-13x \ge 2\left| {:\left( {-13} \right) < 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x \le -\dfrac{2}{{13}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\left( {-\infty ;-\dfrac{2}{{13}}} \right].} \right.\)

Ответ: \(\left( {-\infty ;\;-\dfrac{2}{{13}}} \right].\)