Answer
$\left( -2,\dfrac{6}{5} \right)$
Work Step by Step
Since for any $a\gt0$, $|x|\le a$ implies $-a\le x\le a$, then the given inequality, $
|5x+2|\lt8
,$ is equivalent to
\begin{array}{l}\require{cancel}
-8\lt 5x+2\lt8
\\\\
-8-2\lt 5x+2-2\lt8-2
\\\\
-10\lt 5x\lt6
\\\\
-\dfrac{10}{5}\lt \dfrac{5}{5}x\lt\dfrac{6}{5}
\\\\
-2\lt x\lt\dfrac{6}{5}
.\end{array}
Hence, the solution set is $
\left( -2,\dfrac{6}{5} \right)
.$
See graph below.
