1. **State the problem:** Solve the equation $$\frac{x}{2} + \frac{x}{3} = 10$$ 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. **Rewrite the equation:** $$\frac{5x}{6} = 10$$ 7. **Solve for $x$ by multiplying both sides by 6:** $$6 \times \frac{5x}{6} = 10 \times 6$$ $$\cancel{6} \times \frac{5x}{\cancel{6}} = 60$$ $$5x = 60$$ 8. **Divide both sides by 5:** $$\frac{5x}{5} = \frac{60}{5}$$ $$\cancel{5}x = 12$$ $$x = 12$$ **Final answer:** $x = 12$