Question

Sa se rezolve inecuatia:
|2x+5| (|4x+7|-20)<0

Answer 1

$\it |2x+5|(|4x+7|-20)<0 \Rightarrow \begin{cases} \it 2x+5\ne0 \Rightarrow 2x\ne-5\Rightarrow x\ne-\dfrac{5}{2}\ \ \ \ \ (1)\\ \\ \\ \it |4x+7|-20<0 \Rightarrow |4x+7|<20\ \ \ \ \ (2)\end{cases}\\ \\ \\ (2) \Rightarrow -20<4x+7<20|_{-7} \Rightarrow -27<4x<13|_{:4} \Rightarrow -\dfrac{27}{4}< x<\dfrac{13}{4}\ \ \ \ (3)\\ \\ \\ (1),\ (3) \Rightarrow x\in \Big(-\dfrac{27}{4},\ \ \dfrac{13}{4}\Big)\setminus \Big\{-\dfrac{5}{2}\Big\}$