If the reciprocal of x is between 0 and 1, which of the following must be true?

Correct answer marked below

x^3 < x^6 < x^7

Correct

x^6 < x^3 < x^7

x^3 < x^7 < x^5

x^3 < x^7 < x^6

x^7 < x^3 < x^6

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Comments

YousefSep 5

Reciprocal between 0 and 1 means x itself has to be bigger than 1, right? Once I got that the exponents just sort themselves out.

SivamanojSep 18

yeah exactly, once x>1 the bigger exponent wins so it's pretty quick

LavanyaSep 7

wait why is (A) ordering them smallest to largest? I keep second guessing because x^7 looks huge. but i guess with x>1 that's the point lol

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.