Answer
$\left[ -7,13 \right]$
Work Step by Step
Since for any $a\gt0$, $|x|\le a$ implies $-a\le x\le a$, then the given inequality, $
|-3+x|\le10
,$ is equivalent to
\begin{array}{l}\require{cancel}
-10\le -3+x \le10
\\\\
-10+3\le -3+3+x \le10+3
\\\\
-7\le x \le13
.\end{array}
Hence, the solution set is $
\left[ -7,13 \right]
.$
See graph below.