Answer
$[-1,2].$
Work Step by Step
$-|1-2x|\geq-3$, so $|1-2x|\leq3$,
so $-3\leq1-2x\leq3$,
so $-4\leq-2x\leq2$,
so $2\geq x\geq-1$, thus the solution set is: $[-1,2].$
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