Answer
$(-\infty,-\frac{1}{2})\cup(\frac{7}{2},\infty)$.
Work Step by Step
The given expression is
$\Rightarrow |2x-3|\gt4$
Rewrite the inequality without absolute value bars.
$\Rightarrow 2x-3\lt-4$ or $2x-3\gt4$
Add $3$ to all parts.
$\Rightarrow 2x-3+3\lt-4+3$ or $2x-3+3\gt4+3$
Simplify.
$\Rightarrow 2x\lt-1$ or $2x\gt7$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\lt\frac{-1}{2}$ or $\frac{2x}{2}\gt\frac{7}{2}$
Simplify.
$\Rightarrow x\lt-\frac{1}{2}$ or $x\gt\frac{7}{2}$
The solution set is less than $-\frac{1}{2}$ or greater than $\frac{7}{2}$.
The interval notation is
$(-\infty,-\frac{1}{2})\cup(\frac{7}{2},\infty)$.
