|x|

Question

Hi, I am having this confusion of how the values for this is x>1 & x<-1. What i am doing currently is, for x>0 , x 1 -1

chetan2u · Answer

You cannot cancel out X from both sides.. So the solution would be 1) X>0 X0....X(x-1)>0 Since X>0, x-1>0 or X>1 So range X>0 2) x<0 -x0....X(X+1)>0 Since X<0, X+1<0 or X<-1 So range X<-1

Amanullah Khan · Answer

In 2nd equation, x<0 -x0....X(X+1)>0 there will be 2 equations ... X>0 and X+1>0... in which X+1>0 will become x>-1 ?

chetan2u · Answer

You are starting 2nd equation with X<0, then how can you take X>0

Amanullah Khan · Answer

Sorry, my bad! I was totally confused with something else. Understood it

Thanks for bearing my stupidity :D

JaeTPU · Answer

separate |x|0 , x 1 -1>x (since x is negative, dividing by x flips the inequality)

ccooley · Answer

Generally, you can't 'divide out' a variable from both sides of an inequality, unless you know for sure whether that variable is positive or negative.

So, if you want to simplify something like x < x^2, you'd need to think like this:

- If I know for sure that x is positive, then simplify normally: 1 < x
- If I know for sure that x is negative, then I have to reverse the inequality, since I'm dividing by a negative: 1 > x
- If I don't know whether x is positive or negative, I shouldn't simplify it - or I should simplify it in a different way, without dividing both sides by x. For instance, start by subtracting x from both sides instead.

|x|<x^2 , how do i identify the ranges for this?

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