Answer
$[-5,3]$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | 2(x-1)+4\right |\leq8$
Rewrite the inequality without absolute value bars.
$\Rightarrow -8\leq 2(x-1)+4\leq8$
Solve compound inequality.
Add $-4$ to all three parts.
$\Rightarrow -8-4\leq 2(x-1)+4-4\leq8-4$
Simplify.
$\Rightarrow -12\leq 2(x-1)\leq4$
Divide all three parts by $2$.
$\Rightarrow \frac{-12}{2}\leq \frac{2(x-1)}{2}\leq\frac{4}{2}$
Simplify.
$\Rightarrow -6\leq x-1\leq2$
Add $1$ to all three parts.
$\Rightarrow -6+1\leq x-1+1\leq2+1$
Simplify.
$\Rightarrow -5\leq x\leq3$
The solution set $[-5,3]$.
