This video is going to be about expressing 
inequalities using symbols
and on number lines/
So let's get started...
You know, if I have something like x equals 2,
I can show that a number line
by...
let's make this a number line. The 2 is over here,
all I have to do is
draw a dark circle
and that would tell me that
at the two something's going on,
that x equals 2.
Now instead of that
what if I have something like x is
some number that's greater than 2.
In other words x could be 3 or 4 or
5, it could be two and a half.
Well let's try a number line again...
here's a zero, let's mark where the 2 is,
so x could be any number that's bigger than 2. So I could...
let's say this is a 3...
I could draw a dark circle here, I could draw another dark circle over here,
I could draw a dark circle here, I could draw a dark circle
anywhere along here
ninety two
because x is greater than two and i
don't want to show show they any
talks or or their and
nowhere down here words less than two
so what did you hear is on the clinton
and open circle
to show that i'm not going to be too
and at the end of this client
opportunity carol
to show that this keep going well we're
twisted
so another words i can say for much of
the texas some number of tickets and two
reason to i can show it with this simple
degraded inside
or
i can use any of the line
dark inline everywhere where x is
graders into
sprint open circle enacted to to show
that i'm not talking about the area
and
just disregard everything that's less
than two
now what if i had a situation where cut
taxes great isn't true
or
x
might also equal to
well i can combine both of the symbols
of the great is and symbol he equal
simple
into one sample of my license
x
I've got the greater than sign,
I'm going to put a little line under it, as if I'm taking one of the lines from this equal sign,
and this is going to read
x is greater than
or equal to
2.
And now if I want to show that...
here's my number line...
here's where the 2 is,
so all the places where x is greater
than 2, in other words the 'greater than' part
are going to be over here...
3, 4, 5, 2 and 1/2,
and this line's gonna keep going,
(that should be an arrow)
but it can also be equal to 2,
so instead of an open circle
I'm gonna put a closed circle, I'm gonna fill it in,
because that's what I use when I want to
show that x is equal to 2.
So what I'm doing is I'm combining this,
this closed circle
and this heavy line
with the open circle.
When I combine both of those
I end up with this
and this gives me x
is greater than or equal to 2,
and I used this symbol, the combined symbol,
for x is greater than
or equal to 2.
Okay, well if things can be greater than
something, they can also be less than something
So let's say I want to show that x is
less than
I'll stick with 2.
Well, if x is less than 2...
here's my number line...
here's my 2...
it means x could be 1, it could be over here,
x could be zero, x could be negative 1, it could be negative 2,
it can be anywhere along here
it can't be 2
so I'm gonna put an open circle there
and it can't be any number that's greater than 2.
So I'm gonna take all those number that are less than 2, all those places,
and I'll just darken my line
and I'll draw an arrow to show that I can keep
going
and this will be a way on the number one, 
a graphic way,
of showing that
x is less than 2,
and just as before
maybe I've got a situation where x is less
than 2
or
x is equal to 2.
I can combine these two symbols,
the 'less than' and the 'equal to' symbols
into x is less than
or equal to... in other words I've got the less than sign
and I've got part of the equal sign combined
together...
I'll put the 2 in...
and if I want to show that on the number
line
well here's the place where x is equal
to 2, that was one of my
my possibilities
and everywhere along here
1, 0, negative 1 and so on, everywhere
along here
x is
less than 2,
so
this
a heavy line and a filled-in circle
is how I'm going to express the
inequality x is less than
or equal
to 2,
and that's really all there is to it,
there's only four of these symbols - greater than, 
greater than or equal to, less than,
less than or equal to,
and
there's a this way of putting them on the number line.
So that's gonna be it for now,
take care, I'll see you next time.
