Answer
$\text{the interval } \left( -\infty,-2 \right)\cup \left( 5,\infty \right)
$
Work Step by Step
Since $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$, then the statement $
|2x-3|\gt7
$ evaluates to
\begin{array}{l}
2x-3\gt7\\
2x\gt10\\
x\gt5
,\\\\\text{OR}\\\\
2x-3\lt-7\\
2x\lt-4\\
x\lt-2
.\end{array}
Hence, the solution set is $
\text{the interval } \left( -\infty,-2 \right)\cup \left( 5,\infty \right)
$.
