Chapter 1 - Section 1.6 - Equations and Inequalities Involving Absolute Value - 1.6 Assess Your Understanding - Page 134: 77

$a=-1$ and $b=-\frac{1}{15}$

We are given: $|x-2|\leq 7$ $-7\leq x-2\leq 7$ We add $2$: $-5\leq x\leq 9$ And subtract $10$: $-15\leq x-10\leq-1$ We take the reciprocal: $-\frac{1}{15}\geq\frac{1}{x-10}\geq-1$ $-1\leq\frac{1}{x-10}\leq-\frac{1}{15}$ Therefore: $a=-1$ and $b=-\frac{1}{15}$