Given that $−7 ≤ x ≤ 3$ and $−5 ≤ y ≤ 12$ , what is the range of the product xy?

Correct answer marked below

-84 ≤ xy ≤ 36

Correct

-42 ≤ xy ≤ 36

-36 ≤ xy ≤ 84

-15 ≤ xy ≤ 36

-7 ≤ xy ≤ 36

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Explanation

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Official Explanation

Official

With the constraints

−7 ≤ x ≤ 3

and

−5 ≤ y ≤ 12

, we can determine the range of the product xy. The minimum value occurs at…

Comments

LuisApr 8, 2025

appreciated!

RaymondNov 12, 2024

cheers!

BonSep 19

Why isn't the max just 3×12? That gives 36 which is in every answer choice, so the min is the real question.

TumulSep 20

the max is fine, but for the min you have to check the most negative combo, don't just take -7×-5

What this question tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.