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How Did This Problem Change Signs?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by BlindVision » Wed Mar 25, 2009 6:48 pm
2k = pw - 2w^2

2w^2 - pw + 2k = 0

I thought subtracting 2k from each side would end up a (-) sign in front of 2k, not (+) in front of 2k = 0. Can someone please tell me the rule to this?

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by Neo2000 » Wed Mar 25, 2009 7:05 pm
They didnt subtract 2k from both sides. They subtracted (pw - 2w^2) from both sides

2k = pw - 2w^2

2k - (pw - 2w^2) = (pw - 2w^2 ) - (pw - 2w^2)

2w^2 - pw + 2k = 0
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by BlindVision » Wed Mar 25, 2009 7:27 pm
Thanks for you help. I'm still not getting how a (+) is in front of 2K, even if they subtracted (pw - 2w^2) from both sides. I'm not getting the rule. My brain is having a slow day.lol
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by Neo2000 » Wed Mar 25, 2009 7:38 pm
2k - (pw - 2w^2) = (pw - 2w^2 ) - (pw - 2w^2)

The left hand side now becomes
2k - pw - (-2w^2) which is = 2k - pw + 2w^2

Re-arranging these terms you get

2w^2 - pw + 2k

Since no operation was performed on 2k, 2k retains its original "+" value.
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by BlindVision » Wed Mar 25, 2009 7:53 pm
I got it now. Thank you, Neo2000!
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