College Algebra (10th Edition)

The solution set is {$x|x\geq-6$ and $x\leq6$}.
$|-x|-|4|\leq2$ 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 $x\leq6$}.