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If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y

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ghong14
 Post subject: If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y
 Post Posted: Sun Sep 18, 2011 5:59 pm 
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If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y-1)]-1 ?

(1) x = 2y

(2) x + y > 0

First, let's simplify the question:

The explanation simplified the orignal euqation to (xy)/(x+y)> xy.
Is it posssible to make a further simplification to 1/(x+y) >1 by dividing both sides by (xy)? If so by plugging in the first statemenet you get 1/3y >1 which equals 1>3y or y<1/3. I don't see how knowing y<1/3 is sufficient to solve for the problem.
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ninitina89
 Post subject: Re: If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y
 Post Posted: Sat Sep 24, 2011 12:22 am 
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Hi guy,
Whether you have worked the problem?If you have not,I may help you!

I think the answer is both of them are sufficient to the answer
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ninitina89
 Post subject: Re: If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y
 Post Posted: Sat Sep 24, 2011 12:26 am 
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I mean the two conditions should be together are sufficient to the answer
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messi10
 Post subject: Re: If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y
 Post Posted: Sat Sep 24, 2011 1:35 am 
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Hi ghong14,

ghong14 wrote:
The explanation simplified the orignal euqation to (xy)/(x+y)> xy.
Is it posssible to make a further simplification to 1/(x+y) >1 by dividing both sides by (xy)?


You cannot do the above because you don't know the sign of xy. When you are dealing with inequalities, you cannot divide the equation by a variable unless you know the sign of the variable. The sign is required because if the variable is negative, you need to flip the inequality sign.

The question just says that they are non-zero integers, which means they can be either positive or negative. If x and y have the same sign then xy will be positive and then you can divide without flipping the sign. If they have different signs then xy will be negative and you will need to flip the signs. But you don't know the signs so you cannot simplify it further

Regards

Sunil
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StaceyKoprince
 Post subject: Re: If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y
 Post Posted: Fri Nov 11, 2011 10:24 pm 
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Location: San Francisco
Sunil is right - if you don't know the sign and there's an inequality, don't divide by a variable. :)

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