Answer
$\left( \dfrac{6}{5},2 \right)$
Work Step by Step
For any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$. (The symbol $\lt$ may be replaced with $\le$.)
Using the concept above, the solutions to the given inequality, $
|5x-2|\lt8
,$ is
\begin{array}{l}\require{cancel}
-8\lt 5x-2\lt8
\\\\
-8+2\lt 5x\lt8+2
\\\\
-6\lt 5x\lt10
\\\\
-\dfrac{6}{5}\lt x\lt\dfrac{10}{5}
\\\\
-\dfrac{6}{5}\lt x\lt2
.\end{array}
In interval notation, the solution set is $
\left( \dfrac{6}{5},2 \right)
.$
