If x^3 < x^2, which of the following must be negative?

A. x
B. −x
C. x^5
D. x − 1
E. x^(−1)
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Edited. Thank you.
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Alternatively, we can TEST some values.

We're told that x^3 < x^2
So, one possible value is x = -1

Now let's test the answer choices. We get:
A. -1, which is negative. KEEP
B. −(-1) =1, which is positive. ELIMINATE
C. (-1)^5 = -1, which is negative. KEEP
D. (-1) − 1 = -2, which is negative. KEEP
E. (-1)^(−1) = 1/(-1) = -1, which is negative. KEEP

Okay, we're still left with A, C, D and E

We need to test another value.
Another possible value is x = 1/2
Test the remaining answer choices...
A. 1/2, which is positive. ELIMINATE
C. (1/2)^5 = 1/32, which is positive. ELIMINATE
D. (1/2) − 1 = -1/2, which is negative. KEEP
E. (1/2)^(−1) = 2/1 = 2, which is positive. ELIMINATE

By the process of elimination, the correct answer is D

Cheers,
Brent
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X^3-x^2<0
x^2(x-1)<0

X^2 is always positive
X-1 is negative

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