Answer
The solution is $[-1,2]$
Work Step by Step
$-|2x-1|\geq -3$ Isolate absolute value.
$|2x-1|\leq 3$ Solve absolute value.
$-3\leq2x-1\leq 3$ Solve the compound inequality.
$-3+1\leq2x-1+1\leq 3+1$ Add 1 to each term.
$-2\leq2x\leq 4$
$\frac{-2}{2}\leq\frac{2x}{2}\leq\frac{4}{2}$ Divide each term by 2.
$-1\leq{x}\leq2$
The solution set is {$x| -1\leq{x}\leq2$}.
