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

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Intern
Joined: 15 May 2017
Posts: 13
|x|<x^2 , how do i identify the ranges for this?  [#permalink]

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12 Jun 2018, 01:54
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<x^2 => 1<x
for x<0, -x<x^2 => -1<x

Could anyone help me out where i am going wrong?
Thanks
Math Expert
Joined: 02 Aug 2009
Posts: 7108
Re: |x|<x^2 , how do i identify the ranges for this?  [#permalink]

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12 Jun 2018, 03:32
Amanullah Khan wrote:
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<x^2 => 1<x
for x<0, -x<x^2 => -1<x

Could anyone help me out where i am going wrong?
Thanks

You cannot cancel out X from both sides..
So the solution would be
1) X>0
X<x^2......x^2-x>0....X(x-1)>0
Since X>0, x-1>0 or X>1
So range X>0
2) x<0
-x<x^2.....x^2+X>0....X(X+1)>0
Since X<0, X+1<0 or X<-1
So range X<-1
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 15 May 2017
Posts: 13
Re: |x|<x^2 , how do i identify the ranges for this?  [#permalink]

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12 Jun 2018, 05:53
In 2nd equation,
x<0
-x<x^2.....x^2+X>0....X(X+1)>0
there will be 2 equations ... X>0 and X+1>0... in which X+1>0 will become x>-1 ?
Math Expert
Joined: 02 Aug 2009
Posts: 7108
Re: |x|<x^2 , how do i identify the ranges for this?  [#permalink]

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12 Jun 2018, 06:19
Amanullah Khan wrote:
In 2nd equation,
x<0
-x<x^2.....x^2+X>0....X(X+1)>0
there will be 2 equations ... X>0 and X+1>0... in which X+1>0 will become x>-1 ?

You are starting 2nd equation with X<0, then how can you take X>0
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 15 May 2017
Posts: 13
|x|<x^2 , how do i identify the ranges for this?  [#permalink]

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12 Jun 2018, 06:25
chetan2u wrote:
Amanullah Khan wrote:
In 2nd equation,
x<0
-x<x^2.....x^2+X>0....X(X+1)>0
there will be 2 equations ... X>0 and X+1>0... in which X+1>0 will become x>-1 ?

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

Sorry, my bad! I was totally confused with something else.
Understood it
Thanks for bearing my stupidity :D
Intern
Joined: 17 Jun 2017
Posts: 18
Re: |x|<x^2 , how do i identify the ranges for this?  [#permalink]

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26 Jun 2018, 03:15
1
separate |x|<x^2 into two statements
1. for x>0 , x<x^2 => 1<x
2. for x<0, -x<x^2 => -1>x (since x is negative, dividing by x flips the inequality)
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Re: |x|<x^2 , how do i identify the ranges for this?  [#permalink]

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26 Jun 2018, 10:28
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.
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Re: |x|<x^2 , how do i identify the ranges for this? &nbs [#permalink] 26 Jun 2018, 10:28
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