Answer
$[1,3]$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | x-2\right |+4\leq5$
Subtract $4$ from both sides.
$\Rightarrow \left | x-2\right |+4-4\leq5-4$
Simplify.
$\Rightarrow \left | x-2\right |\leq1$
Rewrite the inequality without absolute value bars.
$\Rightarrow-1 \leq x-2\leq1$
Solve compound inequality.
Add $2$ to all three parts.
$\Rightarrow-1+2 \leq x-2+2\leq1+2$
Simplify.
$\Rightarrow1 \leq x\leq3$
The solution set $[1,3]$.
