Answer
The graph of the solution set is shown below.
Work Step by Step
The given expression is
$\Rightarrow |3x-8|\gt7$
Rewrite the inequality without absolute value bars.
$\Rightarrow 3x-8\lt-7$ or $3x-8\gt7$
Add $8$ to all parts.
$\Rightarrow 3x-8+8\lt-7+8$ or $3x-8+8\gt7+8$
Simplify.
$\Rightarrow 3x\lt1$ or $3x\gt15$
Divide all sides by $3$.
$\Rightarrow \frac{3x}{3}\lt\frac{1}{3}$ or $\frac{3x}{3}\gt\frac{15}{3}$
Simplify.
$\Rightarrow x\lt\frac{1}{3}$ or $x\gt5$
The solution set is less than $\frac{1}{3}$ or greater than $5$.
The interval notation is
$(-\infty,\frac{1}{3})\cup(5,\infty)$.
