Intermediate Algebra (12th Edition)

$\left[ -1,13 \right]$
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $|-x+6|\le7 ,$ is equivalent to \begin{array}{l}\require{cancel} -7\le -x+6 \le7 .\end{array} Using the properties of inequality, then \begin{array}{l}\require{cancel} -7-6\le -x+6-6 \le7-6 \\\\ -13\le -x \le1 \\\\ 13\ge x \ge-1 \\\\ -1\le x \le13 .\end{array} Hence, the solution is the interval $\left[ -1,13 \right] .$