<p>Each of the following inequalities is true for some values of x EXCEPT</p>
<p>a) x< x^2 < x^3
b) x < x^3 < x^2
c) x^2 < x^3 < x
d) x^3 <x <x^2
e) x^3 < x^2 <x</p>
<p>the right answer is D, but I don't get how C isn't the right answer either.</p>
<p>x times x times x is not less than just x</p>
<p>that proves that C is right.</p>
<p>I think the “right” answer is wrong</p>
<p>A. Example x= 2 ~~~ 2 < 4 < 8
B. Example x= -.5 ~~~ -.5< -.125 < .25
C
D. Example x= -2 ~~~ -8 < -2 < 4
E. Example x=.9 ~~~~ .729 < .81 < .9</p>
<p>Try 1 of each “type” of number. There are 4 “types” that I have in mind: </p>
<p>Numbers greater than 1, between 0 and 1, between -1 and 0, and less than -1.</p>
<p>So for example, try 2, 1/2, -1/2, and -2. Each of these numbers will eliminate one answer choice, and you will be left with the answer.</p>
<p>Remark: I suppose I should mention that there are 3 more “degenerate types”: 1, -1, and 0. But these are not needed in this problem.</p>
<p>C)
Using 2: 4<8<2
Using 1/2: 1/4<1/8<1/2
Using -1/2: 1/4<-/18<-/12
Using -2: 4<-8<-2</p>
<p>D)
Using 2: 8<2<4
Using 1/2: 1/8<1/2<1/4
Using -1/2: -1/8<-1/2<1/4
Using -2: -8<-2<4 <-----THIS WORKS! ?? So how is D right?</p>
<p>so sorry guys. I marked myself wrong, C is the correct answer</p>