#### Answer

$x=12 ~or~x=-12 $.

#### Work Step by Step

Using the definition of the absolute value, we have
$$
\frac{3}{4}|x|=9\Longrightarrow |x|=9\times\frac{4}{3}=12
.$$
Thus, we have the two possible solutions (negative and positive):
$x=12 ~or~x=-12 $.