1. **State the problem:** Solve the equation $$\frac{2x}{5} + \frac{x}{10} = 3$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combine terms easily. 3. **Find common denominator:** The denominators are 5 and 10. The least common denominator (LCD) is 10. 4. **Rewrite fractions with LCD:** $$\frac{2x}{5} = \frac{2x \times 2}{5 \times 2} = \frac{4x}{10}$$ 5. **Rewrite the equation:** $$\frac{4x}{10} + \frac{x}{10} = 3$$ 6. **Combine like terms:** $$\frac{4x + x}{10} = 3$$ $$\frac{5x}{10} = 3$$ 7. **Simplify the fraction:** $$\frac{\cancel{5}x}{\cancel{10}} = \frac{x}{2} = 3$$ 8. **Solve for $x$ by multiplying both sides by 2:** $$x = 3 \times 2$$ $$x = 6$$ **Final answer:** $$x = 6$$