Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding - Page 134: 93

$x=-1$ or $x=5$

$3x-|2x+1|=4 $ or $3x-|2x+1|=-4 $ Thus $3x-4=|2x+1| $ or $3x+4=|2x+1|$ Thus $3x-4=2x+1$ or $3x-4=-(2x+1)$ or $3x+4=2x+1$ or $3x+4=-(2x+1)$ Thus $x=5$ or $5x=3$ (but this is not a solution after substituting back) or $x=-3$ (not a solution after substituting back) or $x=-1$