Answer
$\left( -2,7 \right)$
Work Step by Step
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$, then the solution to the given inequality, $
\left| 2x-5 \right|\lt9
,$ is
\begin{array}{l}\require{cancel}
-9\lt 2x-5\lt9
\\\\
-9+5\lt 2x-5+5\lt9+5
\\\\
-4\lt 2x\lt14
\\\\
-\dfrac{4}{2}\lt \dfrac{2x}{2}\lt\dfrac{14}{2}
\\\\
-2\lt x\lt7
.\end{array}
Hence, the solution set is the interval $
\left( -2,7 \right)
.$