a,
\(\left|4x-x\right|=2x-1\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-x=2x-1\\-\left(4x-x\right)=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-x-2x+1=0\\-4x+x-2x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\-5x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\frac{1}{5}\end{matrix}\right.\)