Question: x - 6 = \frac{x + 9}{6}
1. **State the problem:** Solve the equation $$x - 6 = \frac{x + 9}{6}$$ 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:**
$$6(x - 6) = 6 \times \frac{x + 9}{6}$$
4. **Simplify both sides:**
$$6x - 36 = \cancel{6} \times \frac{x + 9}{\cancel{6}} = x + 9$$
5. **Bring all terms involving $x$ to one side and constants to the other:**
$$6x - x = 9 + 36$$
6. **Simplify:**
$$5x = 45$$
7. **Divide both sides by 5:**
$$\frac{5x}{\cancel{5}} = \frac{45}{\cancel{5}}$$
8. **Final solution:**
$$x = 9$$
**Answer:** $x = 9$