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Inequalities with two inequality signs

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by massi2884 » Tue May 15, 2012 10:48 am
Hi, I have a doubt. How can we manipulate inequalities with two inequality signs?

For example this one: x + 2 < y < x + 6
If I move the numbers to the other side changing the signs, I obtain the following:
x < y -2 - 6 < x

But it looks weird because it's like x < y - 8 < x

Thanks.
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by mathbyvemuri » Tue May 15, 2012 7:21 pm
we can't subtract 2 at one inequality and 6 at another inequality at a time.
x + 2 < y < x + 6
First subtract 2 all over:
x < y-2 < x+4
Then subtract 6 all over:
x-6 < y-8 < x-2

or you can subtract 8 at both inequalities at a time
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by ankita1709 » Tue May 15, 2012 10:01 pm
Another way can be deal with the each of the inequalities separately
y<x+6 and y>x+2

This method is really helpful when there are quadratics or higher power involved
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