Question 7845: Can you explain absolute value to me? I need help solving this problem. -6+2. I think the answer is -4. that is what my workbook says. I also thought an absolute value was never a negitive number. Can you please help me? I'm having lots of trouble because I'm 2 levels above everyone else but I just started so I'm having trouble.
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! Practically, absolute value is how far a number is to 0. In that sense, the absolute value of a number is always greater than or equal to zero, AKA, never negative.
You were right in saying that -6 + 2 = -4. I don't think that had anything to do with absolute value. HOWEVER, if the problem said |-6 + 2|, then your answer would have been 4. The absolute value signs (the "straight parentheses") actually do tell you to perform what's inside it first, so, calculate the -6 + 2 first. That gives you a -4. This -4 is inside the absolute value sign: |-4|. When you see that, it really means "how far is -4 from 0" and the answer is 4. It just ends up being a fact that you make the number positive when you take it outside the absolute value signs.
It gets quite tricky when they throw in variables and expressions in there. For example, you may encounter in the near future a problem like |x - 7| = 5. It looks just like x - 7 = 5, and x will be 12. Will |12 - 7| equal 5? Yes, indeed, because |12 - 7| = |5| = 5 (5 is 5 away from 0). HOWEVER, there is another answer besides x = 12. If we showed that |5| = 5, then isn't |-5| also equal to 5? So it makes sense to also set whatever's inside the absolute value equal to -5. SO, x - 7 = -5. With this one, x = 2. You think? Alright. Let's plug the 2 inside: |2 - 7| ?= 5 ---> |2 - 7| = |-5| = 5. True. So the absolute value will almost always make you have two solutions. In this case, x = 12 and x = 2.
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