Answer
$\left( -\dfrac{8}{5},2 \right)$
Work Step by Step
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$, then the expression, $
\left| 5x-1 \right|\lt9
,$ is equivalent to
\begin{array}{l}\require{cancel}
-9\lt 5x-1\lt9
\\\\
-9+1\lt 5x-1+1\lt9+1
\\\\
-8\lt 5x\lt10
\\\\
-\dfrac{8}{5}\lt \dfrac{5}{5}x\lt\dfrac{10}{5}
\\\\
-\dfrac{8}{5}\lt x\lt2
.\end{array}
Hence, the solution set is $
\left( -\dfrac{8}{5},2 \right)
.$
