Answer
$(-\infty,-3)\cup(12,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | 3-\frac{2x}{3}\right |\gt5$
Rewrite the inequality without absolute value bars.
$\Rightarrow 3-\frac{2x}{3}\lt-5$ or $3-\frac{2x}{3}\gt5$
Solve each inequality separately.
Subtract $3$ from all parts.
$\Rightarrow 3-\frac{2x}{3}-3\lt-5-3$ or $3-\frac{2x}{3}-3\gt5-3$
Simplify
$\Rightarrow -\frac{2x}{3}\lt-8$ or $-\frac{2x}{3}\gt2$
Multiply all parts by $-3$ and change the sense of the inequality.
$\Rightarrow -\frac{2x}{3}(-3)\gt-8(-3)$ or $-\frac{2x}{3}(-3)\lt2(-3)$
Simplify.
$\Rightarrow 2x\gt24$ or $2x\lt-6$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\gt\frac{24}{2}$ or $\frac{2x}{2}\lt\frac{-6}{2}$
Simplify.
$\Rightarrow x\gt12$ or $x\lt-3$
The solution set is less than $-3$ or greater than $12$.
The interval notation is
$(-\infty,-3)\cup(12,\infty)$.
