Chapter 4 - Section 4.3 - Equations and Inequalities Involving Absolute Value - Exercise Set - Page 283: 38

{$-3,\dfrac{5}{3}$}

Given: $\dfrac{x}{2}-2=x-\dfrac{1}{2}$ or,$\dfrac{x}{2}-x=-\dfrac{1}{2}+2$ or, $ x=-3$ Now, $\dfrac{x}{2}-2=-(x-\dfrac{1}{2})$ or, $\dfrac{x}{2}-2=-x+\dfrac{1}{2}$ or,$\dfrac{x}{2}+x=\dfrac{1}{2}+2$ or, $ x=\dfrac{5}{3}$ Hence, {$-3,\dfrac{5}{3}$}