Задача 7. Решите неравенство \(2\left( {x + 1} \right) > 3\left( {x + 2} \right)-4\)
Ответ
ОТВЕТ: \(\left( {-\infty ;\;0} \right).\)
Решение
\(2\left( {x + 1} \right) > 3\left( {x + 2} \right)-4\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x + 2 > 3x + 6-4\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,-x > 0\left| {:\left( {-1} \right) < 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x < 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\left( {-\infty ;0} \right).} \right.\)
Ответ: \(\left( {-\infty ;\;0} \right).\)