Answer
$(−∞,-1]\cup[4,∞)$.
The graph of the solution set is shown below.
Work Step by Step
The given expression is
$\Rightarrow |2x-3|\geq5$
Rewrite the inequality without absolute value bars.
$\Rightarrow 2x−3\leq−5$ or $2x−3\geq5$
Solve each inequality separately.
Add $3$ to all parts.
$\Rightarrow 2x−3+3\leq−5+3$ or $2x−3+3\geq5+3$
Simplify.
$\Rightarrow 2x\leq−2$ or $2x\geq8$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{−2}{2}$ or $\frac{2x}{2}\geq\frac{8}{2}$
Simplify.
$\Rightarrow x\leq-1$ or $x\geq4$
The solution set is less than or equal to $-1$ or greater than or equal to $4$.
The interval notation is
$(−∞,-1]\cup[4,∞)$.
The combined graph is shown below.
