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Inequalities

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Inequalities [#permalink] New post 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
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x2 -4 less than 0.png
x2 -4 less than 0.png [ 15.14 KiB | Viewed 501 times ]

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Re: Inequalities [#permalink] New post 25 Oct 2013, 01:32
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Re: Inequalities [#permalink] New post 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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