Question: 7/3 m + 6 + 1/3 m + 14 = 5(1/3 m + 2)
1. **State the problem:** Solve the equation $$\frac{7}{3}m + 6 + \frac{1}{3}m + 14 = 5\left(\frac{1}{3}m + 2\right)$$ for $m$.
2. **Combine like terms on the left side:**
$$\frac{7}{3}m + \frac{1}{3}m + 6 + 14 = \frac{8}{3}m + 20$$
3. **Expand the right side using distributive property:**
$$5 \times \frac{1}{3}m + 5 \times 2 = \frac{5}{3}m + 10$$
4. **Rewrite the equation:**
$$\frac{8}{3}m + 20 = \frac{5}{3}m + 10$$
5. **Subtract $$\frac{5}{3}m$$ from both sides:**
$$\frac{8}{3}m - \frac{5}{3}m + 20 = 10$$
6. **Simplify the left side:**
$$\frac{3}{3}m + 20 = 10$$
$$m + 20 = 10$$
7. **Subtract 20 from both sides:**
$$m + \cancel{20} - \cancel{20} = 10 - 20$$
$$m = -10$$
**Final answer:**
$$m = -10$$