Answer
$\left[ -2,9 \right]$
Work Step by Step
Since for any $a\gt0$, $|x|\le a$ implies $-a\le x\le a$, then the given inequality, $
|2x-7|\le11
,$ is equivalent to
\begin{array}{l}\require{cancel}
-11\le 2x-7\le11
\\\\
-11+7\le 2x-7+7\le11+7
\\\\
-4\le 2x\le18
\\\\
-\dfrac{4}{2}\le \dfrac{2}{2}x\le\dfrac{18}{2}
\\\\
-2\le x\le9
.\end{array}
Hence, the solution set is $
\left[ -2,9 \right]
.$
See graph below.