the modem
We'll take a look at my number line here.
In the center
you have 0. To the right you have all the
positive numbers
and to the left you have all the
negative numbers. Positive and negative
numbers on the number line are called
integers
and I like us to do some comparing
of these numbers, keeping in mind that
the one to the right is always
larger. Think of your bank account as
having
0 in it and anything above zero is good.
You've got money in your checking account.
If you have anything in the negative that
means you're overdrawn.
Now here's the interesting thing that we
sometimes forget. As the numbers
get. . .appear to get larger, as we go
to the left with our negative numbers,
they are in fact
getting smaller. You're overdrawn by a
dollar,
but, it's much worse to be overdrawn by
ten dollars. So, the higher the numbers go,
the smaller they get. So, let's do some
comparison with our,
inequality signs. Let's say I have
a negative 2 is less than
0.  Well, a negative ,  here's a -2
and here's 0.  0 is to the right so
-2 is less than zero how about
negative 7 is
less than a -4
here's -4 on the number line
and you can see that is to the right
of the -7
so and -7 is less than
-4 let's try
Oh let's say 6 is
greater than 0
6 is to the right of 0 and
6 is greater than 0 okay let's try
ok let's try just a  couple more. how about  umm
negative 1 is
greater than negative
-9
negative 1 is to the right of negative 9 some
people also looking so what's closer to
zero
well that's nice over negative side  but
that doesn't really work on the right
hand side
so always go with the number to the
right of another number is larger
so -1 is greater them a negative 9
alright know about a -4
is less than 2  here's the 2 on the
number line
and -4 is to the left or
2 is to the right of -4
so that's a true statement -4 is less than 2
alright so let's also look at
something called absolute value
let me write that for you absolute
value a sample of it would look like
this
absolute value
simply means how many jumps
to get back to zero so it's it's not
it's never negative not negative jumps
but positive jumps its just
jumps back to zero so if I were to
give you this if I were to say what is
the absolute value of 5
I would go over to 5
and I would count how many jumps to get
back to zero I'm at 5
1,2,3,4,5
it is 5 jumps to get back to zero so I'll
bring it
out of its absolute value sign
the answer is 5 the absolute value
of a negative 3
says let's go to a  -3 on the number line
right here and how many jumps to get back
to zero
1,2,3
so the negative 3 comes out of a positive 3
so it doesn't matter
if you have fractions
or decimals or whole numbers it always
comes out
positive  let me give it some more examples
the absolute value
of 1/2
it comes out as 1/2
the absolute value
-11 how many jumps back to 0
from -11 will bring 11 bring it out of
the absolute value bars
and maybe have umm 4.2
well it is 4.2 jumps back to
0 so I'll bring absolute
value
for 4. 2
absolute value is always always always
going to be positive there's a but
coming
but we will talk about that minute alright
now let's compare some numbers when
they're in absolute value
we've already been compare numbers just
plain numbers
now we're gonna do it in absolute value
let's say that we have
an absolute value of a negative 7
is being compared to an absolute value
of 5 you cannot compare numbers in
absolute value to you bring them
out about absolute value bars so I will
bring the -7 out as a positive 7
I'll bring the five out as a positive five  because that's how my jumps
back 0
now that I have brought them out of absolute value 7
is greater than 5 and I'll put my
greater than sign or I could do my greater than less than greater
or equal to sign  okay
let's try another one
let's say that I have
4.7 in  absolute value
and I would like to compare it to
a negative 4.3
an absolute value okay
doesn't matter if it's possible negative
it always is going to come out how
that's right as I positive so this comes
down
as 4.7
this comes out as 4.3
4.7 is greater than 4.3
so we'll put our inequality sign in
right there
alright; I'll let's try
let's try one where one them is absolute
value  one of them is not
so we have a negative 17
and I'm comparing it to
a 16 well there's nothing to worry
about sixteen still 16
but absolute value over -17 is what
that's true it is a positive 17
positive 17 so it comes out as a
positive
and I'm comparing it now to a 16 and 17  is
and  greater than 16
so remember when you're doing absolute
value
you always bring the number out of the 
absolute value signs
and make a positive when you're
comparing numbers that are in absolute
value
bring them out first and then compare
them
the mom
