truongynhi wrote:

Hi chetan2u,

Thank you for the prompt reply. But I still have a doubt.

Take the inequation \(x^2<4\) for example. We then have \(|x|<2\), which means \(-2<x<2\). What I understand is that x must be greater than -2 AND less than 2 for the inequalitiy to hold. So I think this is an AND scenario.

If, however, \(x^2>4\), then \(x<-2\) OR \(x>2\). This is clearly an OR scenario. Here OR makes sense to me.

My inequality skill is pretty rusty. Thank you for bearing with me. I very appreciate your help!

Hi

truongynhi,

I am happy to help you and clear a few doubts you have..

WHAt does OR and AND mean..

1) Take the inequation \(x^2<4\) for example. We then have \(|x|<2\), which means \(-2<x<2\)

So here too you had 2 inequalities, x<2 and x>-2..

x<2 can mean x is -3 so this is a solution when we are using OR since we are not looking at both together..

But here x<2 and x>-2 has a range which OVERLAPS, so this is the combined solution for two inequalities..

when you are choosing a value in this range, you are using AND, since taht value will satisfy both the inequalities..

2)If, however, \(x^2>4\), then \(x<-2\) OR \(x>2\). This is clearly an OR scenario.

YES, this is OR situation, because there is no overlap and hence there is no possiblity of a combined solution..

any solution will satisfy just one inequality..

Now when you have two variable as in the case of Q mentioned here..

3+y≤x≤3−y.. you cannot take this as a solution..

WHY..

because the two inequalities you have combined have come in two different scenarios of OR while taking value of x..

there is no OVERLAP in values of x.. x<3 for one inequality and x>= 3 for other..

so don't combine the two..
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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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