# Absolute value formula

#### bbm25

##### New member

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.

#### topsquark

##### Full Member
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

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

#### bbm25

##### New member

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

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

#### pka

##### Elite Member
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

##### Elite Member
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

##### New member
No, it says |x|= -x. Now, what is -x when x= -3?
Thank you so much. This is a very clear explanation.

#### bbm25

##### New member
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!