\(\left|2x-1\right|-x=4\)
\(\Leftrightarrow\left|2x-1\right|=4+x\)
\(\Leftrightarrow\orbr{\begin{cases}2x-1=4+x\\2x-1=-4+x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-x=4+1\\2x-x=-4+1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\x=-3\end{cases}}\)
Vậy \(x\in\left\{5;-3\right\}\)