Inequalities with a Negative Fraction

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If , then each of the following must be true EXCEPT

Review: Inequalities with a Negative Fraction


Explanation

In this question, a has two key attributes: first, that it is negative, and second, that is a fraction of absolute value less than one. The first fact means that it will be positive at even powers and negative at odd powers, like any negative number. The fractional nature means that its absolute value gets smaller as it's taken to higher powers, although, since it's also negative, it still flops back and forth between positive and negative. Digging in, (A) is true, because ; the first is left of the other on the number line. Choice (B) is correct, because . Choice (C) is correct, because is left of on the number line. Choice (E) correct in a similar way to (C). Choice (D) says that , which is false.

The correct answer is (D).


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