Answer
$\left( -3,3 \right)
Work Step by Step
Using the properties of equality, the given expression, $
9+\left| 5x \right|\lt24
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left| 5x \right|\lt24-9
\\\\
\left| 5x \right|\lt15
.\end{array}
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$, then the expression, $
\left| 5x \right|\lt15
,$ is equivalent to
\begin{array}{l}\require{cancel}
-15\lt 5x\lt15
\\\\
-\dfrac{15}{5}\lt \dfrac{5}{5}x\lt\dfrac{15}{5}
\\\\
-3\lt x\lt3
.\end{array}
Hence, the solution set is $
\left( -3,3 \right)
.$
