Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 29

$$m=\frac{13}{9}\quad \mathrm{or}\quad \:m=3$$

Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find: $$20-9m=-7\quad \mathrm{or}\quad \:20-9m=7 \\ m=\frac{13}{9}\quad \mathrm{or}\quad \:m=3$$