Answer
$\text{the interval } \left[ -\dfrac{9}{4},\infty \right)$
Work Step by Step
Since $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$, then the statement $
|9+4x|\ge0
$ evaluates to
\begin{array}{l}
9+4x\ge0\\
4x\ge-9\\\\
x\ge-\dfrac{9}{4}
.\end{array}
Hence, the solution set is $
\text{the interval } \left[ -\dfrac{9}{4},\infty \right)
$.
