If -0.5 < x < 0, which of the following must be true?
I. x^7 < x^2
II. x^3 < 1 – x^3
III. x^4 < x^2	Choose the most appropriate option.
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^7 &lt; x^2 --&gt; from -0.5 &lt; x &lt; 0 it follows that LHS&lt;0<rhs, --="" 1="" <="" ii.="" is="" so="" statement="" this="" true.="" x^3="" –=""> x^3(1+1) &lt; 1 --&gt; negative*positive &lt; 0 &lt; 1, so this statement is also true.   III. x^6 &lt; x^2 --&gt; reduce by x^2 (we can safely do that since from -1 &lt; x &lt; 0 is follows that x^4&gt;0): x^4 &lt; 1. Again, as -1 &lt; x &lt; 0, then x^4 must be less than 1. Hence, this statement is also true.   Answer: I, II and III.</rhs,>
<result>E</result>
If -0.5 < x < 0, which of the following must be true?
I. x^7 < x^2
II. x^3 < 1 – x^3
III. x^4 < x^2