1. **State the problem:** Solve the equation $\frac{x}{2} + \frac{x}{3} = 9$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combine terms easily. 3. **Find the common denominator:** The denominators are 2 and 3, so the least common denominator (LCD) is 6. 4. **Rewrite each fraction with denominator 6:** $$\frac{x}{2} = \frac{3x}{6}, \quad \frac{x}{3} = \frac{2x}{6}$$ 5. **Combine the fractions:** $$\frac{3x}{6} + \frac{2x}{6} = \frac{3x + 2x}{6} = \frac{5x}{6}$$ 6. **Set the equation:** $$\frac{5x}{6} = 9$$ 7. **Solve for $x$ by multiplying both sides by 6:** $$\cancel{6} \times \frac{5x}{\cancel{6}} = 9 \times 6$$ $$5x = 54$$ 8. **Divide both sides by 5:** $$\frac{5x}{\cancel{5}} = \frac{54}{\cancel{5}}$$ $$x = \frac{54}{5}$$ 9. **Final answer:** $$x = \frac{54}{5} = 10.8$$