Answer
The solution set is {$x|x\geq-6 $ and $x\leq6$}.
Work Step by Step
$|-x|-|4|\leq2$ Simplify
$|-x|-4\leq2$ Isolate the absolute value.
$|-x|-4+4\leq2+4$ Add 4 both sides.
$|-x|\leq6$ Solve absolute value
$-6\leq-x\leq6$
$\frac{-6}{-1}\geq\frac{-x}{-1}\geq\frac{6}{-1}$Divide each term by -1 and reverse the inequality symbols.
$6\geq{x}\geq-6$
$x\geq-6 $ and $x\leq6$
The solution set is {$x| x\geq-6 $ and $x\leq6$}.
