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Absolute Value: MGMAT QBank Question

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RonPurewal
 Post subject: Re: Still Confused abt Statement 1- Would appreciate any hel
 Post Posted: Sat Nov 15, 2008 7:12 am 
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ManhattanGMAT Staff


Posts: 7146
earthling wrote:
Guys,

I am confused with Stacy's remark "Scenario 3: One positive, one negative. And now I've already got an idea of the range of numbers I should be testing, because Scenario 1 resulted in x < -1 and Scenario 2 resulted in x > 1. So... let's see what would happen if x is between those two numbers. For |x + 1|, if -1 < x < 1, then the contents will be positive. For |x –1|, if -1 < x < 1, then the contents will be negative. "

Why wouldn't you test two more scenarios i.e. Left Side is negative and right sand is positive or Right Side is -ve and left side is positive. This we can establish the condition that x not equal to 1. I guess my confusion is what condition are we testing in Stacy's remark for scenario 3? How does it help in knowing that the left side is positive and right is -ve?

Any help will be appreciated. Thanks


(x + 1) is (x - 1) plus two. therefore, it's impossible for (x + 1) to be negative while (x - 1) is positive.
since this "fourth case" is impossible, you don't have to consider it.

by the way:
this is a rather complicated way to solve this equation. for an absolute value equation involving other terms, such as |expression| + other stuff = |expression|, you might need an approach like that.

but for this one, it's sufficient just to consider two possibilities: either (x + 1) and (x - 1) have the same sign, or they have opposite signs. in fact, you can just set the equations up in that way; you don't even have to figure out what the actual signs are.

see here. i'm not sure why there are 2 live threads on this problem, but that's the breaks.
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