1. **State the problem:** Solve the equation $$\frac{5}{2}x - 7 = \frac{3}{4}x + 14$$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We can do this by moving all terms involving $x$ to one side and constants to the other. 3. **Subtract $\frac{3}{4}x$ from both sides:** $$\frac{5}{2}x - \frac{3}{4}x - 7 = 14$$ 4. **Find a common denominator to combine $x$ terms:** $$\frac{10}{4}x - \frac{3}{4}x - 7 = 14$$ 5. **Combine like terms:** $$\left(\frac{10}{4} - \frac{3}{4}\right)x - 7 = 14$$ $$\frac{7}{4}x - 7 = 14$$ 6. **Add 7 to both sides:** $$\frac{7}{4}x - \cancel{7} + 7 = 14 + 7$$ $$\frac{7}{4}x = 21$$ 7. **Multiply both sides by the reciprocal of $\frac{7}{4}$, which is $\frac{4}{7}$:** $$x = 21 \times \frac{4}{7}$$ 8. **Simplify:** $$x = \cancel{21}^3 \times \frac{4}{\cancel{7}^1} = 3 \times 4 = 12$$ **Final answer:** $x = 12$ The correct choice is D. x = 12.