Absolute Value of Integers

Find the absolute value
of x when x is equal to 5,

x is equal to negative 10,
and x is equal to negative 12.

So the absolute value,
the way of writing it

is almost more complicated
than what it really is.

The absolute value is really
just the distance of x from 0.

So let me just draw a fast
number line over here.

So let's just put
0 right over here,

since we're thinking
about the distance from 0.

So let's just think
about the absolute value.

Let's think about
the absolute value

of x when x is equal to 5.

So that's equivalent to
the absolute value of 5.

We just substituted 5 for x.

The absolute value of 5 is
the distance of 5 from the 0.

So you go 1, 2, 3, 4, 5.

5 is exactly 5 to
the right of 0.

So the absolute
value of 5 is just 5.

Now I think you
already get to see

this is a pretty
straightforward concept.

Now let's do something a
little more interesting,

the absolute value of x when
x is equal to negative 10.

So let's just put
negative 10 in for x.

This is the distance that
negative 10 is from 0.

And so let's just go negative
1, negative 2, negative 3,

negative 4, negative 5, negative
6, negative 7, negative 8,

negative 9, negative 10.

I should extend the
number line more.

So this right here
is negative 10.

So how far is it away from 0?

Well, it's 10 to the left of 0.

So you put a 10 here.

And so in general,
absolute value

will always be a
positive quantity.

And when we're rethinking
about just absolute values

of just numbers, it's
just going to be,

really, the positive
version of that number.

Let's do one more.

Well, they tell us to do one
more, the absolute value of x

when x is equal to negative 12.

So we have the absolute
value of negative 12.

We don't even to look
at the number line.

It's just going to be
the positive version

of negative 12.

It's just going
to be equal to 12.

And this is just saying that
negative 12 is 12 away from 0.

And we could draw it over here.

This is negative 11.

Negative 12 is right over here.

It is 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12 away from 0.