\(\Leftrightarrow\left[{}\begin{matrix}2x-3=x-1\\2x-3=1-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)
\(\left|2x-3\right|=\left|x-1\right|\\ \Rightarrow\left[{}\begin{matrix}2x-3=x-1\\2x-3=1-x\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)