1. **State the problem:** Solve the equation $$\frac{35}{x} = \frac{5}{2}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products are equal. So, $$35 \times 2 = 5 \times x$$ 3. **Calculate the cross products:** $$70 = 5x$$ 4. **Isolate $x$ by dividing both sides by 5:** $$x = \frac{70}{5}$$ 5. **Simplify the fraction:** $$x = \cancel{\frac{70}{5}} = 14$$ 6. **Conclusion:** The solution to the equation is $x = 14$. This matches the second answer choice.