Absolute value formula

bbm25

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IMG_0337.JPG

What i understand:
1) absolute value = distance on the number line
2) absolute value is always positive

But this formula says the absolute value of x when x is less than 0 is negative?? And it also makes no mention of any number line.

Please help?
 

topsquark

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You are correct when you say that absolute value needs to be positive. Think about what that means when x is negative. If |x| = x for negative x then the absolute value would be a negative number, which is absurd. Thus |x| = -x, returning a positive value.

-Dan
 

HallsofIvy

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The negative of a negative number is positive. For example, when x is -3, |x|= |-3|= -(-3)= 3.
 

bbm25

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Thank you for your responses!

The negative of a negative number is positive. For example, when x is -3, |x|= |-3|= -(-3)= 3.
But from what i understand, that's not what the picture says. What the picture says is |x| = -3
 

HallsofIvy

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No, it says |x|= -x. Now, what is -x when x= -3?
 

pka

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But from what i understand, that's not what the picture says. What the picture says is |x| = -3
Lets suppose that \(\displaystyle f(x)=1-x\).
\(\displaystyle f(4)=-3\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle f(-4)=5\) Do you have any doubt whatsoever about that? If you do please post it.

Now suppose that \(\displaystyle g(x)=-x\)
\(\displaystyle g(4)=-4\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle g(-4)=-(-4)=4\) Do you have any doubt whatsoever about that? If you do please post it.

Now suppose that \(\displaystyle h(x)=|x|\)
\(\displaystyle h(4)=4\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle h(-4)=4\) Do you have any doubt whatsoever about that? If you do please post it.
 

Jomo

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Just for exactness, it is not always true that the absolute value of a number is always positive. The absolute value of a number (like 0) can be 0. The correct statement is that the absolute value of a number is never negative.

If you put a negative sign in front of a number it is not always negative. For example -3 IS a number and if I put a negative sign in front of it, -(-3), it becomes 3 which is positive.
 

bbm25

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bbm25

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Lets suppose that \(\displaystyle f(x)=1-x\).
\(\displaystyle f(4)=-3\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle f(-4)=5\) Do you have any doubt whatsoever about that? If you do please post it.

Now suppose that \(\displaystyle g(x)=-x\)
\(\displaystyle g(4)=-4\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle g(-4)=-(-4)=4\) Do you have any doubt whatsoever about that? If you do please post it.

Now suppose that \(\displaystyle h(x)=|x|\)
\(\displaystyle h(4)=4\) Do you have any doubt whatsoever about that? If you do please post it.
\(\displaystyle h(-4)=4\) Do you have any doubt whatsoever about that? If you do please post it.
This was very clear. Thank you so much for writing this!
 
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