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Inequality question

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by Stockmoose16 » Thu Aug 21, 2008 1:56 pm
In the MGMAT inequality book, it states that you can't simply isolate the X variable in the following equation, because it could be + or -:

xy<3y

Instead, it says you should factorize the equation:

xy-3y<0

=y(x-3)<0

Then it says, "y and x-3 have opposite signs"... where did they come up with that?

Isn't x-3<0, which means x<3 (meaning, it could be a positive or negative number...

And y<0, which means it's negative.

Why is the book saying that they have opposite signs? They MAY have opposite signs, but that's not definitive, right?

What would be the correct answer to the original question?
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by parallel_chase » Thu Aug 21, 2008 2:29 pm
Here are four rules of inequalities that will help you answer above question:

(+)*(-) < 0 ----I
(-)*(+) < 0 ----II
(-)*(-) > 0 ----III
(+)*(+)>0 ----IV


y(x-3)<0

if y is positive, x-3 has to be negative
if y is negative, x-3 has to be positive
refer to cases I & II

Thats why it says "y and x-3 have opposite signs".

Hope this helps. Let me know if you still have any doubts.
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