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Inequation HELP

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by ricaototti » Wed Sep 03, 2008 9:49 pm
Why is the solution of x^2 < 4 equivalent to -2<x<2???

Can someone please carefully and step by step explain it to me so I understand the concept behind it?

Thanks. I really appreciate it!

One more quick question, how accurate are the mock exams from 800score, Veritas and Amcor?
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by hengirl03 » Thu Sep 04, 2008 12:04 am
Since x is 2, x can be positive or negative. Keep this in mind when solving for x.

Solving for x when x positive:

Step 1:Take the square root of both sides
(x)^2 < 4 (Take the square root of x)
x < 2



Solving for x when x negative:

Step 1:Take the square root of both sides
(-x)^2 < 4

Step 2: Solve for x. Keep in mind that when you divide an inequality by a negative number, you switch the inequality sign
-x < 2
x>-2



So -2<x<2


I hope this helps



As for your exam question, I'm not really familar with the ones that you listed. But I've heard that the best practice exams are the one by GmatPREP, Manhattan , and Kaplan. Especially the GmatPrep one, since it gives real Gmat questions that have been retired.
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by vish150783 » Thu Sep 04, 2008 6:34 am
I have a conceptual question on this...

When you take a square root on both the sides how come you don't consider +/- on both the sides of the equations?

i.e. if X^2 < 4 then

+/- X < +/- 2 right? Because we dont want to prematurely assume that sqrt of 4 is 2.

that gives us a four possibilities..

+X < +2; +X< -2; -X< +2; -X<-2

1. X<2
2. X<-2
3. X>-2
4. X>2.

why do I get four contradicting answers?
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by Ian Stewart » Thu Sep 04, 2008 7:56 am
There is a different way to look at this:

x^2 < 4
x^2 - 4 < 0
(x+2)(x-2) < 0

So x+2 and x-2 have opposite signs: one is negative, the other is positive. Since x-2 is clearly smaller than x+2, x-2 must be negative, and x+2 must be positive:

x-2 < 0 ----> x < 2
x+2 > 0 ----> x > -2

So -2 < x < 2
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by vish150783 » Thu Sep 04, 2008 11:08 am
thanks a lot Ian. I think the main concept here is that x is a variable so we do not know anything about it.

So, when I did

X^2 = +/- X its wrong..we cannot assume this since X is to be value which we need to find out not something we know.

So, only its safe to assume sqrt of 4 is +/-2.

X<2 or X<-2, so in this case X<2 or X>-2 since X is negative in the second scenario.
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by vish150783 » Thu Sep 04, 2008 11:12 am
thanks a lot Ian. I think the main concept here is that x is a variable so we do not know anything about it.

So, when I did

X^2 = +/- X its wrong..we cannot assume this since X is to be value which we need to find out not something we know.

So, only its safe to assume sqrt of 4 is +/-2.

X<2 or X<-2, so in this case X<2 or X>-2 since X is negative in the second scenario.
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