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Fun with inequalities

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Intern
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Joined: 14 May 2010
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Fun with inequalities [#permalink] New post 07 Jul 2010, 04:42
Hey there

Could you possibly help me with an induction which I couldn't understand, it was off an MGMAT CAT

The questions involves the expression

|x|xy + 9 > 0 // and we will later plaug in -1 for y

I can see how that is the same as

|x|xy > -9

And after plugging in -1, I can see how that becomes

|x|x (-1) > -9

And I can see how after diving by -1, which is a negative number the inequality becomes

|x|x < 9

What I can't get, is that the inequality, according to the solution was not reduced to

|x|x < 9 after division by -1

But instead, it was reduced to

x < 9

BOOOOM !! How did that happen ? :)

Since we are on this, I identified one of my weak points to be SPECIFICALLY inequalities/modulus in DS questions, how can I improve in this area ?

P.S I am not sure whether this post needs to go here or under Math problems, please let me know so I can make sure it sits in the right place
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Ms. Big Fat Panda
Ms. Big Fat Panda
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Re: Fun with inequalities [#permalink] New post 07 Jul 2010, 05:59
Do you think you could just post the actual question? Thanks.
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Re: Fun with inequalities [#permalink] New post 07 Jul 2010, 07:39
Hey whiplash, yeah ofcourse

So its a DS question

- If |x|xy + 9 > 0 , and x and y are integers, is x < 6

1) y is negative
2) y <= 1


The inquiry i posted is specifically about MGMAT's explanation for statement one (they happen to chose -1 as an example) and as they were reducing the inequality, they jumped from this

|x|x (-1) > -9

to this

x < 9

as opposed to

|x|x < 9

So I am not sure how they induced that

Thanks a lot
Ms. Big Fat Panda
Ms. Big Fat Panda
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Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
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Re: Fun with inequalities [#permalink] New post 07 Jul 2010, 08:50
That sounds kind of inconsistent, actually. Maybe it was just a printing mistake?
Re: Fun with inequalities   [#permalink] 07 Jul 2010, 08:50
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