Answer
The solution set is $\{-2,\frac{4}{5}\}$.
Work Step by Step
The given equation is
$\left | 5x+3 \right |=7$
Remove absolute value bar.
$5x+3=-7$ or $5x+3=7$
Add $-3$ to both sides.
$5x+3-3=-7-3$ or $5x+3-3=7-3$
Simplify.
$5x=-10$ or $5x=4$
Divide both sides by $5$.
$\frac{5x}{5}=-\frac{10}{5}$ or $\frac{5x}{5}=\frac{4}{5}$
Simplify.
$x=-2$ or $x=\frac{4}{5}$.
