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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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