\(\Rightarrow\left|x+1\right|=2x-\dfrac{1}{2}\\ \Rightarrow\left[{}\begin{matrix}x+1=2x-\dfrac{1}{2}\left(x\ge-1\right)\\x+1=\dfrac{1}{2}-2x\left(x< 1\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\left(tm\right)\\x=-\dfrac{1}{6}\left(tm\right)\end{matrix}\right.\)
\(2x-\left|x+1\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left|x+1\right|=2x-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=2x-\dfrac{1}{2}\left(x\ge-1\right)\\x+1=\dfrac{1}{2}-2x\left(x< -1\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-x=-\dfrac{3}{2}\\3x=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\left(nhận\right)\\x=-\dfrac{1}{6}\left(loại\right)\end{matrix}\right.\)
