Answer
$x=-\dfrac{9}{4}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
|9+4x|=0
$ evaluates to
\begin{array}{l}
9+4x=0\\
4x=-9\\\\
x=-\dfrac{9}{4}
.\end{array}
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