AlgebraVery hardLeast value of a linear combination over bounded variables
Algebra practice question
If 2 ≤ x ≤ 5 and −3 ≤ y ≤ 1, what is the least possible value of x − 2y?
Answer: 0
x − 2y is least when x is least and y is greatest: 2 − 2(1) = 0.
Common wrong answers
- If you answered 8
- 8 is x − 2y at x = 2, y = −3, the least x with the least y, but a smaller y makes −2y larger.
- If you answered 11
- 11 is the greatest value (5 − 2(−3)).
- If you answered -4
- −4 comes from x = 2 and y = 3, but y is at most 1.
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