Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 27

$x=\frac{27}{2} ~or~x=-\frac{27}{2} $.

Using the definition of the absolute value, we have $$ \frac{2}{3}|x|=9\Longrightarrow |x|=9\times\frac{3}{2}=\frac{27}{2} .$$ Thus, we have the two possible solutions (negative and positive): $x=\frac{27}{2} ~or~x=-\frac{27}{2} $.