Answer
$(-\infty,-1]\cup[2,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow 3\leq \left | 2x-1\right |$
Switch sides.
$\Rightarrow \left | 2x-1\right | \geq 3$
Rewrite the inequality without absolute value bars.
$\Rightarrow 2x-1\leq-3$ or $2x-1\geq3$
Solve each inequality separately.
Add $1$ to all parts.
$\Rightarrow 2x-1+1\leq-3+1$ or $2x-1+1\geq3+1$
Simplify.
$\Rightarrow 2x\leq-2$ or $2x\geq4$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{-2}{2}$ or $\frac{2x}{2}\geq\frac{4}{2}$
Simplify.
$\Rightarrow x\leq-1$ or $x\geq2$
The solution set is less than or equal to $-1$ or greater than or equal to $2$.
The interval notation is
$(-\infty,-1]\cup[2,\infty)$.
