\(\left|x-1\right|-2x=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x-1-2x=\dfrac{1}{2}\\x-1-2x=\dfrac{-1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-x-1=\dfrac{1}{2}\\-x-1=\dfrac{-1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=\dfrac{-1}{2}\end{matrix}\right.\)