Answer
The solution is $−4\leq w \leq -\frac{4}{3}$.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 2|3w+8|-13\leq -5$
Add $13$ to each side.
$\Rightarrow 2|3w+8|-13+13\leq -5+13$
Simplify.
$\Rightarrow 2|3w+8|\leq 8$
Divide each side by $2$.
$\Rightarrow |3w+8|\leq 4$
Write a compound inequality.
$\Rightarrow 3w+8\leq 4$ and $3w+8\geq -4$
Subtract $8$ from each side.
$\Rightarrow 3w+8-8\leq 4-8$ and $3w+8-8\geq -4-8$
Simplify.
$\Rightarrow 3w\leq -4$ and $3w\geq -12$
Divide each side by $3$.
$\Rightarrow w\leq -\frac{4}{3}$ and $w\geq -4$
Hence, the solution is $−4\leq w \leq -\frac{4}{3}$.
