If -3 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^5 < 2 – x
III. x^4 < x^2
Choices:
A) I only  B) I and II only  C) II and III only  D) I and III only  E) I, II and III
I. x^5 &lt; x^2 --&gt; since x is always negative x^5 is always negative and x^2 is always positive therefore x^5 &lt; x^2, so this statement is true.   II. x^5 &lt; 2 – x --&gt; x(x^4+1) &lt; 2 --&gt; negative*positive &lt; 0 &lt; 2, so this statement is also true.   III. x^4 &lt; x^2 --&gt; reduce by x^2 (we can safely do that since from -3 &lt; x &lt; 0 is follows that x^2&gt;0): x^2 &lt; 1. Since -3 &lt; x &lt; 0, then x^2 can be greater than 1. Hence, this statement is false.   Answer: I and II only.
<result>B</result>
If -3 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^5 < 2 – x
III. x^4 < x^2