Answer
$-6\leq v \leq 3$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow \frac{2}{3}|4v+6|-2\leq 10$
Add $2$ to each side.
$\Rightarrow \frac{2}{3}|4v+6|-2+2\leq 10+2$
Simplify.
$\Rightarrow \frac{2}{3}|4v+6|\leq 12$
Multiply each side by $\frac{3}{2}$.
$\Rightarrow \frac{3}{2}\cdot \frac{2}{3}|4v+6|\leq \frac{3}{2}\cdot 12$
Simplify.
$\Rightarrow |4v+6|\leq 18$
Write a compound inequality.
$\Rightarrow 4v+6\leq 18$ and $4v+6\geq -18$
Subtract $6$ from each side.
$\Rightarrow 4v+6-6\leq 18-6$ and $4v+6-6\geq -18-6$
Simplify.
$\Rightarrow 4v\leq 12$ and $4v\geq -24$
Divide each side by $4$.
$\Rightarrow \frac{4v}{4}\leq \frac{12}{4}$ and $\frac{4v}{4}\geq -\frac{24}{4}$
Simplify.
$\Rightarrow v\leq 3$ and $v\geq -6$
Hence, the solution is $-6\leq v \leq 3$.