1. **State the problem:** Solve for the unknown variable $x$ in each proportion given by the figures. 2. **Recall the proportion rule:** If two ratios are equal, then their cross products are equal, i.e., if $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. 3. **Solve each proportion:** **Problem 9:** Given $\frac{x}{2} = \frac{6}{3}$ Cross multiply: $$x \times 3 = 2 \times 6$$ $$3x = 12$$ Divide both sides by 3: $$\cancel{3}x = \frac{12}{\cancel{3}}$$ $$x = 4$$ **Problem 10:** Given $\frac{21}{14} = \frac{x}{12}$ Cross multiply: $$21 \times 12 = 14 \times x$$ $$252 = 14x$$ Divide both sides by 14: $$\cancel{14} \times 18 = \frac{252}{\cancel{14}} = x$$ $$x = 18$$ **Problem 11:** Given $\frac{27}{9} = \frac{36}{x}$ Cross multiply: $$27 \times x = 9 \times 36$$ $$27x = 324$$ Divide both sides by 27: $$\cancel{27}x = \frac{324}{\cancel{27}}$$ $$x = 12$$ **Problem 13:** Given $\frac{2x - 4}{15} = \frac{12}{20}$ Cross multiply: $$(2x - 4) \times 20 = 15 \times 12$$ $$20(2x - 4) = 180$$ $$40x - 80 = 180$$ Add 80 to both sides: $$40x = 260$$ Divide both sides by 40: $$\cancel{40}x = \frac{260}{\cancel{40}}$$ $$x = 6.5$$ **Problem 14:** Given $\frac{8}{5} = \frac{x}{10}$ Cross multiply: $$8 \times 10 = 5 \times x$$ $$80 = 5x$$ Divide both sides by 5: $$\cancel{5} \times 16 = \frac{80}{\cancel{5}} = x$$ $$x = 16$$ **Final answers:** - Problem 9: $x = 4$ - Problem 10: $x = 18$ - Problem 11: $x = 12$ - Problem 13: $x = 6.5$ - Problem 14: $x = 16$