Answer
The solution set is {$x| x\geq-1$ or $x\leq-3$}.
Work Step by Step
$|-x-2|\geq1$ Solve absolute value.
$-x-2\geq1$ or $-x-2\leq-1$
$-x-2+2\geq1+2$ or $-x-2+2\leq-1+2$ Add 2 to both sides of each inequality.
$-x\geq3$ or $-x\leq1$
$\frac{-x}{-1}\leq\frac{3}{-1}$ or $\frac{-x}
{-1}\geq\frac{1}{-1}$ Divide by -1 and reverse the inequality symbol.
$x\leq-3$ or $x\geq-1$
The solution set is {$x| x\geq-1$ or $x\leq-3$}.
