\(\left|x-2\right|-\left|2x+3\right|-x=-2\)
\(\Rightarrow\left|x-2\right|-\left|2x+3\right|=-2+x\)
+) Nếu x \(\ge\) 2 \(\Rightarrow\left\{{}\begin{matrix}x-2\ge0\\2x+3\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left|x-2\right|=x-2\\\left|2x+3\right|=2x+3\end{matrix}\right.\)
\(\Rightarrow x-2-\left(2x+3\right)=-2+x\)
\(\Rightarrow x-2-2x-3-x=-2\)
\(\Rightarrow-2x-5=-2\Rightarrow-2x=3\Rightarrow x=\dfrac{-3}{2}\)( ko t/m x \(\ge\) 2 ) => loại
+) Nếu \(-\dfrac{3}{2}\le x< 2\Rightarrow\left\{{}\begin{matrix}x-2< 0\\2x+3\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left|x-2\right|=-x+2\\\left|2x+3\right|=2x+3\end{matrix}\right.\)
\(\Rightarrow-x+2-\left(2x+3\right)=-2+x\)
\(\Rightarrow-x+2-2x-3-x=-2\)
\(\Rightarrow-4x-1=-2\)
\(\Rightarrow-4x=-1\Rightarrow x=\dfrac{1}{4}\) ( t/m \(-\dfrac{3}{2}\le x< 2\) )
+) Nếu \(x< -\dfrac{3}{2}\Rightarrow\left\{{}\begin{matrix}x-2< 0\\2x+3< 0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-2\right|=-x+2\\\left|2x+3\right|=-2x-3\end{matrix}\right.\)
\(\Rightarrow-x+2-\left(-2x-3\right)=-2+x\)
\(\Rightarrow-x+2+2x+3-x=-2\)
\(\Rightarrow x-x+5=-2\Rightarrow-2=5\) ( vô lý ) => loại
Vậy x = \(\dfrac{1}{4}\)
