AlgebraHardLargest integer x allowed by two inequalities
Algebra practice question
The system y > 2x − 3 and y < x + 2 has solutions (x, y) in the xy-plane. What is the largest integer value of x for which there is some y that satisfies both inequalities?
Answer: 4
A y exists only when 2x − 3 < x + 2, that is x < 5; the largest integer is 4.
Common wrong answers
- If you answered 2
- 2 is where the boundary lines' y-values differ by 3, not the limit.
- If you answered 3
- 3 works but is not the largest.
- If you answered 5
- 5 gives 7 < y < 7, which no y satisfies.
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