Question: x - 5 = \frac{x + 8}{6}
1. **State the problem:** Solve the equation $x - 5 = \frac{x + 8}{6}$ for $x$.
2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the denominator to eliminate the fraction.
3. **Multiply both sides by 6:**
$$6(x - 5) = 6 \times \frac{x + 8}{6}$$
4. **Simplify:**
$$6x - 30 = x + 8$$
5. **Bring all $x$ terms to one side and constants to the other:**
$$6x - x = 8 + 30$$
6. **Simplify:**
$$5x = 38$$
7. **Divide both sides by 5:**
$$\cancel{5}x = \frac{38}{\cancel{5}}$$
8. **Final solution:**
$$x = \frac{38}{5}$$
**Answer:** $x = \frac{38}{5}$ or $7.6$.