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# Absolute value and number lines

## Video transcript

We're told to plot these values
on a number line. And you see every one of
these values have an absolute value sign. So let's take a little bit of
a review of what absolute value even is. The way I think about
it, there's two ways to think about it. The first way to think about
it is, how far is something from 0? So let me plot this
negative 3 here. So let me do a number line. This isn't the number line for
our actual answer, or to this command-- plot these values
on a number line. I'm just first going to plot
the numbers inside the absolute value sign, and then
we're going to take the absolute value and plot those,
just like they're asking us to do. So on this number line, if this
is 0, if we go to the negative, we're going to
go to the left of 0. So this is negative 1, negative
2, negative 3. Negative 3 sits right over
there, so this is negative 3 right there. The absolute value of negative
3 is essentially saying, how far are you away from 0? How far is negative 3 from 0? And you say, well, it's
1, 2, 3 away from 0. So you'd say that the absolute
value of negative 3 is equal to positive 3. Now that's really the conceptual
way to imagine absolute value. How far are you away from 0? But the easy way to calculate
absolute value signs, if you don't care too much about the
concept, is whether it's negative or positive, the
absolute value of it's always going to be positive. Absolute value of negative
3 is positive 3. Absolute value of positive
3 is still positive 3. So you're always going to get
the positive version of the number, so to speak. But conceptualy, you're just
saying how far away are you from 0. So let's do what they asked. So that first value, on this
number line, so all of these are absolute values. So they're all going to
be positive values. So they're all going to
be greater than 0. So let me draw my number
line, like this. I can do a straighter number
line than that. Let's see. Well, that's a little
bit straighter. And let's say, if this is 0,
this would be negative 1, then you'd have 1, 2,
3, 4, 5, 6, 7. I think that'll do the trick. So this first quantity here--
I'll do it in orange --the absolute value of negative 3,
we just figured out, that is positive 3. So I'll plot it right over
there, positive 3. Then this next value, right
here, the absolute value of 7. If we look over here,
1, 2, 3, 4, 5, 6, 7. 7 is how far away from 0? It is 7 away from 0. So the absolute value
of 7 is equal to 7. So you already see the
pattern there. If it's negative, it just
becomes positive. If it's already positive,
it just equals itself. So plotting this value,
I'll just place it right over there. So the absolute value
of 7 is 7. Absolute value of negative
3 is positive 3. Let me mark out the 0 a little
bit better, so you see relative to 0. Now we have the absolute
value of 8 minus 12. Well, first of all, let's figure
out what 8 minus 12 is. So if you take 12 away from
8, you're at negative 4. 12 less than 8 is negative 4. And you can do that on a number
line if you don't quite remember how to do this. But if you, you know, if you
take 8 away from 8, you're at 0, and then you take another
one, you're at negative 1, negative 2, negative 3, all
the way to negative 4. So this is equal to the absolute
value of negative 4. If we just plot negative 4, we
go 1, 2, 3, negative 4 is right over there. But if we're taking its absolute
value, we're saying how far is negative 4 from 0? Well it's 4 away from 0. 1, 2, 3, 4. So this is equal
to positive 4. So we'll plot it right here. This number line is the answer
to this command up here. So the absolute value of 8 minus
12, which is negative 4, is positive 4. Then we have the absolute
value of 0. So how far is 0 from 0? Well, it's 0 away from 0. The absolute value of 0 is 0, so
you can just plot it right over there. And we have one left. Let me pick a suitable
color here. The absolute value
of 7 minus 2. Well, 7 minus 2 is 5, so this
is the same thing as the absolute value of 5. How far is 5 away from 0? Well, it's just 5 away. It's almost, you
know, too easy. That's what makes
it confusing. If I were to plot 5,
it's 1, 2, 3, 4, 5. It is 1, 2, 3, 4,
5 spaces from 0. So the absolute value
of 5 is 5. So you plot it just like that. So conceptually, it's how
far you are away from 0. But if you think about it in
kind of just very simple terms, if it's a negative
number, it becomes a positive version of it. If it's a positive number
already, it just equals itself when you take the
absolute value.