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I know this is a super basic question but I can't find an answer. Is it that the result of anything within $|\quad|$ must be evaluated first and given a positive value?

I knew this years ago but I've forgotten. So for...

y = 2|x + 2| where x = -3....

y = 2

Correct?

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Yes. It's right! –  user21436 Jan 20 '12 at 17:33
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Ok - so implies same order of operations as parenthesis, but result must be evaluated as positive? –  Calvin Froedge Jan 20 '12 at 17:35
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2 Answers

up vote 4 down vote accepted

Yes, you must first evaluate the value of expression in the || (which named absolute) and then if the value is negative multiply it by -1

see here for more information.

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Yes, you must evaluate what is inside of the absolute value symbols first, and then just use the magnitude of that value.

Hence, in algebra, say

|x + 2| = y / 2

can have two possibilities:

x + 2 = y / 2

and

-x - 2 = y / 2

Be careful of this you must. (This wasn't your question, but I thought that this point was important to address.)

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