1. **State the problem:** We are given two trapezoids with corresponding sides and need to find the value of $x$ using proportions. 2. **Identify the correct proportion:** The sides correspond as follows: smaller trapezoid top = 8 inches, bottom = 5 inches; larger trapezoid top = $x$, bottom = 7.5 inches. 3. The proportion that relates $x$ to the other sides is $$\frac{5}{8} = \frac{7.5}{x}$$ because the bottom side of the smaller trapezoid corresponds to the bottom side of the larger trapezoid, and the top side of the smaller trapezoid corresponds to the top side of the larger trapezoid. 4. **Solve the proportion:** $$\frac{5}{8} = \frac{7.5}{x}$$ Cross multiply: $$5 \times x = 8 \times 7.5$$ $$5x = 60$$ Divide both sides by 5: $$x = \frac{60}{5} = 12$$ 5. **Answer:** The value of $x$ is 12 inches. This method uses the property of proportions that corresponding sides of similar figures are proportional.