1. **State the problem:** Ani is 3 years younger than Dion. The sum of their ages is at most 50 years. We need to find the maximum possible age of Ani 5 years ago. 2. **Define variables:** Let $D$ be Dion's age and $A$ be Ani's age. 3. **Express relationship:** Ani is 3 years younger than Dion, so: $$A = D - 3$$ 4. **Form the inequality:** The sum of their ages is at most 50: $$A + D \leq 50$$ 5. **Substitute $A$ in inequality:** $$ (D - 3) + D \leq 50 $$ 6. **Simplify:** $$ 2D - 3 \leq 50 $$ 7. **Solve for $D$:** $$ 2D \leq 53 $$ $$ D \leq 26.5 $$ 8. **Find $A$ using $A = D - 3$:** $$ A \leq 26.5 - 3 = 23.5 $$ 9. **Find Ani's age 5 years ago:** $$ A - 5 \leq 23.5 - 5 = 18.5 $$ **Final answer:** The maximum possible age of Ani 5 years ago is $18.5$ years. **Summary:** a. The linear inequality is $$ (D - 3) + D \leq 50 $$ or $$ 2D - 3 \leq 50 $$. b. The maximum possible age of Ani 5 years ago is $18.5$ years.