Answer
$\left( -\dfrac{7}{5},\dfrac{3}{5} \right)$
Work Step by Step
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the solution to the given equation, $
\left| 5x+2 \right|-2\lt3
,$ is
\begin{array}{l}\require{cancel}
\left| 5x+2 \right|\lt3+2
\\\\
\left| 5x+2 \right|\lt5
\\\\
-5\lt 5x+2\lt5
\\\\
-5-2\lt 5x+2-2\lt5-2
\\\\
-7\lt 5x\lt3
\\\\
-\dfrac{7}{5}\lt \dfrac{5x}{5}\lt\dfrac{3}{5}
\\\\
-\dfrac{7}{5}\lt x\lt\dfrac{3}{5}
.\end{array}
Hence, the solution set is the interval $
\left( -\dfrac{7}{5},\dfrac{3}{5} \right)
.$
