Inequalities : GMAT Quantitative Section
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# Inequalities

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Intern
Joined: 05 Jun 2013
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24 Oct 2013, 22:05
Hello guys,

I have a very silly question for you.

Say we have an equation, (x-2)(x+2) < 0
What would be its solution?

I solve it this way

either (x-2)<0 and (x+2)>0
So, x<2 and x> -2
or
(x-2)>0 and (x+2)<0
x>2 and x<-2

So when I plot a graph it'd look like this
(attaching the image)

now what
What's the solution if I go this way of plotting a graph?
What is the solution at all? since no area of the numberline actually intersects??

its a very lengthy and confusing process.

I need to get my basics right about inequalities problems.
can someone give me links to inequalities concepts?

thanks,
infymys
Attachments

x2 -4 less than 0.png [ 15.14 KiB | Viewed 951 times ]

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Status: It always seems impossible until it's done!!
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Location: India
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25 Oct 2013, 01:32
Hi,

You may read through these post for better understanding of inequalities.

1.http://gmatclub.com/forum/inequalities-basics-154285.html
2. http://gmatclub.com/forum/graphic-approach-to-problems-with-inequalities-68037.html
3. http://gmatclub.com/forum/inequations-inequalities-part-154664.html
4.http://gmatclub.com/forum/inequations-inequalities-part-154738.html
5. http://gmatclub.com/forum/tips-and-tricks-inequalities-150873.html
6.http://gmatclub.com/forum/quick-way-to-graph-inequalities-76255.html

And plenty of them still in the forum, Use the tag search for browsing the theories.. Also please use the right forum to post the questions.

Moderators. Please move this post right forum
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26 Oct 2013, 12:31
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Hi Infymys,

Your approach to solve this question is right and you have reached to the solution.

The answer to this problem is:
either (x<2 and x> -2), say R1 or (x>2 and x<-2), say R2.

If we consider only integer values, then

R1 = {-1, 0, 1} &
R2 = {..., -5, -4, -3, 3, 4, 5, ...}

x can be any one of these numbers.

So, possible values of x are {..., -5, -4, -3, -1, 0, 1, 3, 4, 5, ...}

For this problem, you can not find a single value of x. The value of x lies in a range.

If you will pick any value in this range, it will satisfy the equation (x - 2)(x + 2) < 0

For example, let x=1, then (x - 2)(x + 2) = (1 - 2)(1 + 2) = (-1)(3) = -3 (which is less than 0).

For a value, which is not there in the range, (in this case, -2 & 2), it will not satisfy the equation.

When x=-2, (x - 2)(x + 2) = (-2 - 2)(-2 + 2) = (-4)(0) = 0 (does not satisfy the equation).
Re: Inequalities   [#permalink] 26 Oct 2013, 12:31
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