Answer
$-11\leq x \leq 17$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |x-3|\leq 14$
Write a compound inequality.
$\Rightarrow x-3\leq 14$ and $x-3\geq -14$
Add $3$ to each side.
$\Rightarrow x-3+3\leq 14+3$ and $x-3+3\geq -14+3$
Simplify.
$\Rightarrow x\leq 17$ and $x\geq -11$
Hence, the solution is $-11\leq x \leq 17$.
