Anaira Mitch wrote:If -1 < x < 0, which of the following must be true?
I. x^3 < x^2
II. x^5 < 1 - x
III. x^4 < x^2
a)I only
b)I and II only
c) II and III only
d) I and III only
e) I, II and III
-1 < 0 < 1 indicates that x is a NEGATIVE FRACTION.
Since x is a negative value, x^(even power) = POSITIVE.
As a result, the inequalities above can be safely divided by ANY EVEN POWER OF X.
I:
x³ < x²
x³/x² < x²/x²
x < 1.
Since x is a negative fraction, it must be true that x < 1.
Eliminate C, since it does not include Statement I.
II:
x� < 1-x
x�/x� < (1-x)/x�
x < (1-x)/x�
negative < (positive - negative)/(positive)
negative < positive/positive
negative < positive.
Since a negative value must be less than a positive value, Statement II must be true.
Eliminate A and D, since they do not include Statement II.
III:
x� < x²
x�/x² < x²/x²
x² < 1.
Since x is a negative fraction, it must be true that x² < 1.
Eliminate B, since it does not include Statement III.
The correct answer is
E.
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