Absolute value formula

bbm25

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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?
 
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
 
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
 
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.
 
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.
 
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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