Answer
$\left[ -6,-3 \right]$
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, $
|2x+9|\le3
,$ is
\begin{array}{l}\require{cancel}
-3\le 2x+9\le3
\\\\
-3-9\le 2x+9-9\le3-9
\\\\
-12\le 2x\le-6
\\\\
-\dfrac{12}{2}\le \dfrac{2x}{2}\le-\dfrac{6}{2}
\\\\
-6\le x\le-3
.\end{array}
Hence, the solution set is the interval $
\left[ -6,-3 \right]
.$