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Equations with absolute values - MGMAT

Expert replies
by AleksandrM » Sun Aug 17, 2008 1:44 pm
|x - 9/2| = 5/2

For the above equation, I calculated:

For x < 0

-x + 9/2 = 5/2

x = 2 [not true, because x is less than 0]

For x > 0

x - 9/2 = 5/2

x = 7 [true, because x is greaterthan 0]

However, according to MGMAT, both are correct. I want to understand why I am incorrect.

Thanks.
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Source: — Problem Solving |

by bourne159 » Sun Aug 17, 2008 2:00 pm
Can you post the entire question?

The equation is |X-9/2| = 5/2
When you solve this the two cases are X-9/2 > 0 and X-9/2 <0
You assumed X > 0 and X <0 which are not the right equations.
Both cases give you two solutions for X.

Is the question asking how many solutions exist for X?
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by AleksandrM » Sun Aug 17, 2008 3:17 pm
The question is irrelevant. Yes, the question does assume that there are two solutions. I am trying to understand WHY not WHETHER.

Thanks.
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