well, you already know an absolute value expression has a ± siblings, so let's proceed without much fuss.
[tex] \bf |2x-5|=4\implies
\begin{cases}
+(2x-5)=4\implies 2x=9\implies x=\cfrac{9}{2}\\[-0.5em]
\hrulefill\\
-(2x-5)=4\implies 2x-5=-4\\[1em]
2x=1\implies x=\cfrac{1}{2}
\end{cases} [/tex]
