1. **Problem 1: Add the fractions $\frac{3}{2}$ and $\frac{5}{6}$.** 2. To add fractions, they must have a common denominator. 3. The denominators are 2 and 6. The least common denominator (LCD) is 6. 4. Convert $\frac{3}{2}$ to a fraction with denominator 6: $$\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}$$ 5. Now add the fractions: $$\frac{9}{6} + \frac{5}{6} = \frac{9 + 5}{6} = \frac{14}{6}$$ 6. Simplify $\frac{14}{6}$ by dividing numerator and denominator by their greatest common divisor 2: $$\frac{\cancel{14}^{7}}{\cancel{6}^{3}} = \frac{7}{3}$$ 7. **Final answer for problem 1:** $\frac{7}{3}$ or $2 \frac{1}{3}$. 8. **Problem 2: Solve the equation $4x - 3 = 11$.** 9. Add 3 to both sides to isolate the term with $x$: $$4x - 3 + 3 = 11 + 3$$ $$4x = 14$$ 10. Divide both sides by 4 to solve for $x$: $$\frac{4x}{\cancel{4}} = \frac{14}{4}$$ $$x = \frac{14}{4}$$ 11. Simplify $\frac{14}{4}$ by dividing numerator and denominator by 2: $$\frac{\cancel{14}^{7}}{\cancel{4}^{2}} = \frac{7}{2}$$ 12. **Final answer for problem 2:** $x = \frac{7}{2}$ or 3.5.