Chapter 1 - Expressions, Equations, and Inequalities - 1-6 Absolute Value Equations and Inequalities - Lesson Check - Page 45: 1

$x = -4$ or $4$

$|-6x| = 24$ There are two cases: Case 1: $-6x = 24$ or Case 2: $-6x = -24$ In Case 1, $x = \frac{24}{-6}$, so $x = -4$ In Case 2, $x = \frac{-24}{-6}$, so $x = 4$ If we substitute both $-4$ and $4$ in for $x$, we can see that the equation is satisfied. So, $x = 4, -4$