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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