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when x<0, |x| = -x...so the first eq becomes Y = -x + (-x) = -2x ?????

When x is negative, you don't replace x with -x; if x is negative, then -x is a positive number. If x is negative, there is a negative sign 'inside' of x.

Now, if x is negative, you can replace |x| with -x, because if x is negative, -x will produce the 'positive equivalent' of x. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

But thanks Ian for this last bit. It made me see |x| in a different light. Never thought you could write |x| as -x when x is negative. Makes perfect sense.

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...

I had an interesting conversation with a friend this morning, and I realized I need to add a last word on the series of posts on my application process. Five key words:...