Answer
$(−∞,−6)∪(0,∞)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left |\frac{2x+6}{3}\right |\gt2$
Rewrite the inequality without absolute value bars.
$\Rightarrow \frac{2x+6}{3}\lt-2$ or $ \frac{2x+6}{3}\gt2$
Solve each inequality separately.
Multiply all parts by $3$.
$\Rightarrow (3)\frac{2x+6}{3}\lt3(-2)$ or $ (3)\frac{2x+6}{3}\gt3(2)$
Simplify.
$\Rightarrow 2x+6\lt-6$ or $ 2x+6\gt6$
Subtract $6$ from all parts.
$\Rightarrow 2x+6-6\lt-6-6$ or $ 2x+6-6\gt6-6$
Simplify
$\Rightarrow 2x\lt-12$ or $ 2x\gt0$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\lt\frac{-12}{2}$ or $ \frac{2x}{2}\gt\frac{0}{2}$
Simplify.
$\Rightarrow x\lt-6$ or $ x\gt0$
The solution set is less than $-6$ or greater than $0$.
The interval notation is
$(−∞,−6)∪(0,∞)$.
