Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 26

$$r=-\frac{25}{2}\quad \mathrm{or}\quad \:r=9$$

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: $$4r+7=-43\quad \mathrm{or}\quad \:4r+7=43 \\ r=-\frac{25}{2}\quad \mathrm{or}\quad \:r=9$$