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. **Rewrite the equation:** $$\frac{3X}{6} + \frac{2X}{6} = 9$$ 6. **Combine the fractions:** $$\frac{3X + 2X}{6} = 9$$ $$\frac{5X}{6} = 9$$ 7. **Multiply both sides by 6 to clear the denominator:** $$\cancel{6} \times \frac{5X}{\cancel{6}} = 9 \times 6$$ $$5X = 54$$ 8. **Divide both sides by 5 to solve for $X$:** $$\frac{\cancel{5}X}{\cancel{5}} = \frac{54}{5}$$ $$X = \frac{54}{5}$$ 9. **Final answer:** $$X = \frac{54}{5} = 10.8$$