Typical Inequality Question, plz help!

[Riya]

If x/|x| < x , then which of the following are true?
a) x>1
b) x>-1
c) |x|<1
d) |x|^2>1

[xyz123]

Is it a)?

[Homer Simpson]

(a) i think

x = 1, they are equal
-1<x<1, LHS is 1 but LHS>RHS
x<-1, again, LHS is a some positive number while RHS is negative

thus x>1

[Riya]

Yes, logically the answer seems to be (a). But if we square both the sides and cancel the x^2 term on both sides, the answer we obtain is (d)  That's the dilemma!

[xyz123]

No then it would be 1< |x|

[Homer Simpson]

agree that |x|^2 > 1 after the squaring thing but consider x = 1/2, -1/2,1,-1  even. then this inequality wont work, right? so i think x>1 is the stronger condition.

[Riya]

It can't be |x|>1 either. If we put x= -2 , the equation given in the question won't be satisfied :/

[Riya]

Ok, thanks :)