Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 22

$$g=-7\quad \mathrm{or}\quad \:g=-\frac{7}{3}$$

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: $$3g+14=-7\quad \mathrm{or}\quad \:3g+14=7 \\ g=-7\quad \mathrm{or}\quad \:g=-\frac{7}{3}$$