16Hit1600
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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