1. **State the problem:** Solve the equation $$\frac{x}{9} = \frac{7}{15}$$ for $x$. 2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $a \times d = b \times c$. 3. **Apply cross-multiplication:** $$x \times 15 = 9 \times 7$$ 4. **Simplify the right side:** $$15x = 63$$ 5. **Solve for $x$ by dividing both sides by 15:** $$x = \frac{63}{15}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 3:** $$x = \frac{\cancel{63}^{{21}}}{\cancel{15}^5}$$ 7. **Final answer:** $$x = \frac{21}{5}$$ The correct choice is (B) $x = \frac{21}{5}$.