Answer
The solution is $\Big(-\dfrac{7}{5},\dfrac{3}{5}\Big)$
Work Step by Step
$|5x+2|-2\lt3$
Take $2$ to the right side of the inequality:
$|5x+2|\lt3+2$
$|5x+2|\lt5$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-5\lt5x+2\lt5$
$\textbf{Solve the inequality shown above:}$
$-5\lt5x+2\lt5$
Subtract $2$ from all three parts of the inequality:
$-5-2\lt5x+2-2\lt5-2$
$-7\lt5x\lt3$
Divide all three parts of the inequality by $5$:
$-\dfrac{7}{5}\lt\dfrac{5x}{5}\lt\dfrac{3}{5}$
$-\dfrac{7}{5}\lt x\lt\dfrac{3}{5}$
Expressing the solution in interval notation:
$\Big(-\dfrac{7}{5},\dfrac{3}{5}\Big)$
