AlgebraVery hardLeast integer x for a point in a system of inequalities
Algebra practice question
The point (k, 3) satisfies both y < 2x − 1 and y ≥ −x + 4. What is the least possible integer value of k?
Answer: 3
3 < 2k − 1 gives k > 2, and 3 ≥ −k + 4 gives k ≥ 1. The least integer greater than 2 is 3.
Common wrong answers
- If you answered 1
- 1 satisfies only the second inequality.
- If you answered 2
- 2 makes 2k − 1 equal to 3, not greater than 3.
- If you answered 4
- 4 works but is not the least.
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