Question

Answer 1

\(\left|2x-5\right|+\left|2x+3\right|=8\)

Mặt khác:\(\left|2x-5\right|+\left|2x+3\right|=\left|2x-5\right|+\left|-2x-3\right|\ge\left|2x-5-2x-3\right|=\left|-8\right|=8\)

Nên để thõa mãn yêu cầu thì:

\(\left(2x-5\right)\left(-2x-3\right)\ge0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5\ge0\\-2x-3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5\le0\\-2x-3\le0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow-\dfrac{3}{2}\le x\le\dfrac{5}{2}\)