Inequalities

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Inequalities

by knight247 » Fri Aug 19, 2011 6:47 am
If 4/x<1/3 what is the possible range of values for x?

It's a simple problem from the Manhattan Guide. I've figured out the answer as x<0 and x>12 but I am also able to figure that x>-12. Is that correct?

Let me show u how i get it.
Consider x>0
Then 4/x<1/3
can we re written as x>12

Consider x<0
4/x<1/3 can be re written as 12>x.

But also, since x is negative, it can be written as 12>-x
And, multiplying both sides by -1, I get x>-12. So the range of values for x is -12<x<12....
Is my reasoning correct? Thanks
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by Anurag@Gurome » Fri Aug 19, 2011 6:52 am
knight247 wrote:Consider x<0
4/x<1/3 can be re written as 12>x.

But also, since x is negative, it can be written as 12>-x
And, multiplying both sides by -1, I get x>-12. So the range of values for x is -12<x<12....
Is my reasoning correct? Thanks
No, it's not.
You have to understand that x is never equal to -x whether x is negative or not and hence you cannot just replace x with -x.

We have assumed x to be negative and reached the conclusion that x < 12. This simply means any negative value of x will satisfy the given inequality because any negative value of x is less than 12.

Hope that helps.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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