Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 28

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

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 $.