Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 26

$x=4~or~x=-4$.

Using the definition of the absolute value, we have $$ 5-|\frac{1}{2}x|=3\Longrightarrow |\frac{1}{2}x|=5-3=2 \Longrightarrow \frac{1}{2}x=2~or~ \frac{1}{2}x=-2 .$$ Thus, we have the two possible solutions: $x=4~or~x=-4$.