Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding - Page 134: 78

$a=\frac{1}{7}$ and $b=1$

We are given: $|x+1|\leq 3$ $-3\leq x+1\leq 3$ We add 4: $1\leq x+5\leq 7$ And take the reciprocal: $1\geq\frac{1}{x+5}\geq\frac{1}{7}$ $\frac{1}{7}\leq\frac{1}{x+5}\leq 1$ Therefore: $a=\frac{1}{7}$ and $b=1$