\(4x-5=3-\left|1-x\right|\)
\(\Leftrightarrow3-\left|1-x\right|=4x-5\)
\(\Leftrightarrow-\left|1-x\right|=4x-5-3\)
\(\Leftrightarrow-\left|1-x\right|=4x-8\)
\(\Leftrightarrow\left|1-x\right|=-\left(4x-8\right)\)
\(\Leftrightarrow\left|1-x\right|=-4x+8\)
\(\Leftrightarrow\left[{}\begin{matrix}1-x=-4x+8\\1-x=-\left(-4x+8\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x+4x=8-1\\1-x=4x-8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-x+4x=7\\-x-4x=-8+1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=7\\-5x=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=\dfrac{7}{5}\end{matrix}\right.\)