1. **State the problem:** Tony has 12 dollars to buy apples and bananas. Apples cost 2 dollars per pound, bananas cost 1 dollar per pound. We want to write an inequality to represent how many pounds of apples ($a$) and bananas ($b$) Tony can buy without exceeding 12 dollars. 2. **Write the inequality:** The total cost is $2a + 1b$. Since Tony cannot spend more than 12 dollars, the inequality is: $$2a + b \leq 12$$ 3. **Explain the inequality:** This means the combined cost of apples and bananas must be less than or equal to 12. 4. **Check given points:** - For $a=2$, $b=6$: $2(2) + 6 = 4 + 6 = 10 \leq 12$ (valid) - For $a=4$, $b=4$: $2(4) + 4 = 8 + 4 = 12 \leq 12$ (valid) 5. **Graph description:** The inequality $2a + b \leq 12$ represents the region on or below the line $b = 12 - 2a$ in the coordinate plane where $a$ and $b$ are non-negative. 6. **Two possible combinations:** - 2 pounds of apples and 6 pounds of bananas - 4 pounds of apples and 4 pounds of bananas **Final answer:** $$2a + b \leq 12$$ with possible combinations $(a,b) = (2,6)$ or $(4,4)$.