Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 40

Interval: $(-\infty,\ -3]\ \cup\ [-1,\ \infty)$

$3-|2x+4|\leq 1$ $-|2x+4|\leq 1-3$ $-|2x+4|\leq-2$ $|2x+4|\geq 2$ We split the absolute value into the positive and negative: $2x+4\geq 2$ $ 2x\geq-2$ $ x\geq-1$ $2x+4\leq-2$ $ 2x\leq-6$ $ x\leq-3$ Interval: $(-\infty,\ -3]\ \cup\ [-1,\ \infty)$