Why Do Solutions Sometimes Differ from Absolute Values?

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LindseyM2011
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In equations dealing with absolute value sometimes the answer to the equation does not coorospond with the absolute value. Why is this?
 
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simply put i believe when you have an the absolute value is how far the number is away from zero on the number line. So if you had the absolute value of -4, it would be four.

try this for further understanding, including the real mathmatical definition

http://en.wikipedia.org/wiki/Absolute_value
 

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