1. **State the problem:** We need to determine which values among I. 7.5, II. \frac{22}{3}, and III. 8 satisfy the inequality $$\frac{x}{3} > 2\frac{1}{2}$$. 2. **Rewrite the inequality:** Convert the mixed number to an improper fraction: $$2\frac{1}{2} = \frac{5}{2}$$ So the inequality becomes: $$\frac{x}{3} > \frac{5}{2}$$ 3. **Solve the inequality for $x$:** Multiply both sides by 3 to isolate $x$: $$x > 3 \times \frac{5}{2}$$ $$x > \frac{15}{2}$$ 4. **Simplify the right side:** $$\frac{15}{2} = 7.5$$ 5. **Check each value:** - I. $7.5$: Is $7.5 > 7.5$? No, because it is equal, not greater. - II. $\frac{22}{3} \approx 7.333$: Is $7.333 > 7.5$? No. - III. $8$: Is $8 > 7.5$? Yes. 6. **Conclusion:** Only value III (8) satisfies the inequality. **Final answer:** A III only