1. **State the problem:** Simplify the expression $$\frac{x}{2} + \frac{7x}{6}$$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least common denominator (LCD) of 2 and 6, which is 6. 3. **Rewrite each fraction with the LCD:** $$\frac{x}{2} = \frac{x \times 3}{2 \times 3} = \frac{3x}{6}$$ 4. **Add the fractions:** $$\frac{3x}{6} + \frac{7x}{6} = \frac{3x + 7x}{6} = \frac{10x}{6}$$ 5. **Simplify the fraction:** $$\frac{10x}{6} = \frac{\cancel{2} \times 5x}{\cancel{2} \times 3} = \frac{5x}{3}$$ **Final answer:** $$\frac{5x}{3}$$