Answer
$[-\frac{19}{3},7]$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | 3(x-1)+2\right |\leq20$
Rewrite the inequality without absolute value bars.
$\Rightarrow -20\leq 3(x-1)+2\leq20$
Solve compound inequality.
Add $-2$ to all three parts.
$\Rightarrow -20-2\leq 3(x-1)+2-2\leq20-2$
Simplify.
$\Rightarrow -22\leq 3(x-1)\leq18$
Divide all three parts by $3$.
$\Rightarrow \frac{-22}{3}\leq \frac{3(x-1)}{3}\leq\frac{18}{3}$
Simplify.
$\Rightarrow \frac{-22}{3}\leq x-1\leq6$
Add $1$ to all three parts.
$\Rightarrow \frac{-22}{3}+1\leq x-1+1\leq6+1$
Simplify.
$\Rightarrow \frac{-19}{3}\leq x\leq7$
The solution set $[-\frac{19}{3},7]$.
