Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 36

Interval: $(-\infty,\ -9]\ \cup\ [7,\ \infty)$

$|\displaystyle \frac{x+1}{2}|\geq 4$ $\frac{1}{2}|x+1|\geq 4$ $|x+1|\geq 2*4$ $|x+1|\geq 8$ We split the absolute value into the positive and negative: $x+1\geq 8$ $x\geq 7$ $x+1\leq-8$ $x\leq-9$ Interval: $(-\infty,\ -9]\ \cup\ [7,\ \infty)$