Answer
$(-\infty,-1)\cup(-\frac{1}{5},\infty)$.
Work Step by Step
The given expression is
$\Rightarrow \left | 5x+3\right |\gt2$
Rewrite the inequality without absolute value bars.
$\Rightarrow 5x+3\lt-2$ or $5x+3\gt2$
Solve each inequality separately.
Subtract $3$ from all parts.
$\Rightarrow 5x+3-3\lt-2-3$ or $5x+3-3\gt2-3$
Simplify.
$\Rightarrow 5x\lt-5$ or $5x\gt-1$
Divide all parts by $5$.
$\Rightarrow \frac{5x}{5}\lt\frac{-5}{5}$ or $\frac{5x}{5}\gt\frac{-1}{5}$
Simplify.
$\Rightarrow x\lt-1$ or $x\gt-\frac{1}{5}$
The solution set is less than $-1$ or greater than $-\frac{1}{5}$.
The interval notation is
$(-\infty,-1)\cup(-\frac{1}{5},\infty)$.
