Please help me clarify the definition of absolute value?

👨🏻‍🏫 學術台數學

[匿名]

2006-09-15 3:03 am

The definition of an absolute value is...

|x| = x if x >= 0; |x| = - x if x < 0.

The |x| = -x if x < 0 confuses me. How may an absolute value equal a negative? Please help me clarify.

更新1:

I'm well aware that absolute values can't be negative. The definition I gave is universally known, every math text books has it!

更新2:

DidacticRogue: Thanks a bunch! That clarifies my concern.

回答 (8)

[匿名]

2006-09-15 3:06 am

✔ 最佳答案

The negative of a negative is a positive, so ...

if x < 0 then x is negative

therefore its absolute value is the negation of a negative number

for example,
x = -1

|-1| = -(-1) = 1

Hope this helps!

... and some goober apparently disagrees ... imagine that!

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[匿名]

2006-09-15 3:47 am

first of all DidacticRogue has a good explanation

here is another way of thinking about the absolute value

|x|=+sqrt(x^2) this is a method of finding the absolute value without using an if

examples
x=2
|x|=+sqrt(2^2)=+sqrt(4)=2
x=-2
|x|=+sqrt((-2)^2))=+sqrt(4)=2

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[匿名]

2006-09-15 3:16 am

|x| = x > =0 |x|-x if x<0

like this.

x+1 = 0

solution:

x = -1 (the value of x is -1) the reason why +1 been move to the right then it would be -1 so the result is x = -1

if it is ( + + ) = + ex: (2+2 = 4)
if it is ( - - ) = + ex: (-2-2 = 4)
if it is ( + - ) = - or + ex: (4-2 = 2) , (-6+2 = -4)
(depends on higher number if positive (+) is higher then it would be positive, if negative is higher then it would be negative (-) )

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[匿名]

2006-09-15 3:09 am

a absolute value can't be negative, never.
absolute value is simply the distance away from 0.
Ex #1: l5l = 5
Ex #2: l-6l = 6
Ex#3: l-2.36l = 2.36

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[匿名]

2006-09-15 3:08 am

That is wrong. An absolute Value is how far the number is from zero. So if the number is -7, it is 7 places away from 0, so 7 is your answer. If the number is 2130, the absolute value is 2130, because that is how far away from zero it is. So basically, an absolute value is any #, but w/o the - sign.

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Phoebe

2006-09-15 3:07 am

an absolute value equal a negative when the number inside the | | thing is less than 0
For example :
|3|=? if x<0
then ur answer to this would be -3

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[匿名]

2006-09-15 3:07 am

The |x| = -x if x < 0 part is not correct, the absolute value for any x (+ or -) is x.

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[匿名]

2006-09-15 3:07 am

the absolute value is basically the distance from zero. so the absolute value of -1 is 1 because it is still only 1 away from zero. The absolute value of 15 is 15 because it is fifteen from zero, etc. absolute values are always positive. So really, the absolute value of negative X is X. |x|= x, -x Hope this helps!

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