Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 22

$x=2$

$|3-2x|=|5-2x|$ $3-2x=5-2x$ $\quad$ or $\quad$ $3-2x=-(5-2x)$ $2x-2x=5-3$ $\quad$ or $\quad$ $3-2x=-5+2x$ $0=-2$ $\quad\quad$ or $\quad\quad$ $-4x=-8$ $no~ solution$ $\quad\quad$ and $\quad\quad$ $x=2$