Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 21

$x=-\frac{3}{2}$ $x=-\frac{1}{4}$

$|x-1|=|3x+2|$ We split the absolute value into two equations, the positive and negative: $x-1=3x+2$ $x-3x=2+1$ $-2x=3$ $x=-\frac{3}{2}$ $x-1=-(3x+2)$ $x-1=-3x-2$ $x+3x=-2+1$ $4x=-1$ $x=-\frac{1}{4}$