Question

Giải bpt \(\left|2x-3\right|-x\le1\)

 

 

Answer 1

Gt ⇔ \(\left|2x-3\right|\le x+1\)

⇔ \(\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-3\le x+1\\x\ge\dfrac{3}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}3-2x\le x+1\\x< \dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)

 ⇔\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le4\\x\ge\dfrac{3}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge\dfrac{2}{3}\\x< \dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)

⇔ \(\left[{}\begin{matrix}\dfrac{3}{2}\le x\le4\\\dfrac{2}{3}\le x< \dfrac{3}{2}\end{matrix}\right.\)

⇔ \(\dfrac{2}{3}\le x\le4\)

Vậy bất phương trình có tập nghiệm là

\(S=\left[\dfrac{2}{3};4\right]\)