Absolute value formula

[bbm25]

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]

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]

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

 

[bbm25]

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]

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

 

[pka]

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.

 

[Steven G]

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]

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

Thank you so much. This is a very clear explanation.

 

[bbm25]

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!