reagrding inequalities : GMAT Quantitative Section
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reagrding inequalities

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reagrding inequalities [#permalink]

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New post 28 Apr 2013, 03:51
x^3-x<0
x(x^2-1)<0

I am stuck after this step. Can anyone explain what are possible ranges for the value of x?how to proceed further
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Re: reagrding inequalities [#permalink]

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New post 28 Apr 2013, 04:04
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skamal7 wrote:
x^3-x<0
x(x^2-1)<0

I am stuck after this step. Can anyone explain what are possible ranges for the value of x?how to proceed further



At this point you have to study the sign of \(x\) and \(x^2-1\)
The first is +ve if x>0
The second in +ve is \(x^2-1>0\) so if x>1 or x<-1
Take a look at the picture. Once you have the intervals you intersect them and find the overall sign.
You want the equation to be <0 so you take the -ve intervals => x<-1 and 0<x<1

Hope it's clear, let me know
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Re: reagrding inequalities [#permalink]

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New post 28 Apr 2013, 04:36
thanks a lot..can you please tell me if (X^3-x) >0 then ranges are -1<x <0 and x >1
is it correct?
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Re: reagrding inequalities [#permalink]

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New post 28 Apr 2013, 04:39
thanks a lot..you rock
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Re: reagrding inequalities [#permalink]

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New post 29 Apr 2013, 19:56
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skamal7 wrote:
x^3-x<0
x(x^2-1)<0

I am stuck after this step. Can anyone explain what are possible ranges for the value of x?how to proceed further


Notice that you can further simplify the inequality

x(x+1)(x - 1) < 0

So your transition points are -1, 0 and 1, in that order on the number line.
The negative regions (since there is a less than sign) will be x < -1 and 0 < x < 1.

For more on how we got these ranges, check this post:
http://www.veritasprep.com/blog/2012/06 ... e-factors/
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Re: reagrding inequalities   [#permalink] 29 Apr 2013, 19:56
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