Answer
$\left[ -1,13 \right]$
Work Step by Step
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]
.$
