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>> All right.
Inequalities.
These are what inequalities are.
You have a little symbol here and you can read it
in two different directions.
But if you had 4 and 7, what it is is it's getting smaller
if you look.
This is getting smaller and then going the other direction it's
getting bigger.
So that means this one is the bigger
because it's getting bigger and then that one's getting smaller.
You can see it just go down and down.
It's getting tiny.
That's how you can look at it.
Or you can think of it like before, we had PAC-MAN --
a little vintage here --
but PAC-MAN always eats the bigger number
or you could do the alligator.
And the alligator always eats the bigger number
because there's more meat there.
So that's the direction it's always going to be.
All right?
So if you read it from left to right, we would say
that 4 is less than 7.
And if we change it over here and we put 7
and 4, same two numbers.
We would say 7 is greater than 4
and if you have this one you say 4 is equal to 4.
But it's that is.
You have to use an is in there otherwise it does not mean
an inequality.
You have to say not 4 less than 7, 4 is less than 7,
7 is greater than 4, and 4 is equal to 4.
So very key word.
All right?
And you can read it either way, obviously.
It's how you want to read it.
4 is less than 7, but we're going to start and just read
from left to right to keep it simple.
So 7 is greater than 4.
Always remember the direction.
Okay? All right.
So now it gets a little bit trickier
when you have inequalities.
How do you know which is which?
I mean with integers, how do you know which is bigger
because you see oh, well 17 is bigger than 15 but what
about negative 17 and negative 15?
Now which is bigger?
That's what number lines come in to play.
So a negative 4 would be here and a 4 would be here.
Negatives go on the left and they decrease to the right.
Right? And we increase to the -- sorry -- we decrease to the left
and we increase to the right.
So if you have negative 4 and 4,
you can see that this is why we have this sentence.
Negative 4 is less than 4.
Now here we have 17 and 15.
17 is here, 15 is here.
And if you read it, it says 17 is less.
That's not true is it?
This is a false statement.
So on some of these you're going to be asked
to tell is it true or is it false?
And you just have to look at it.
The bigger number should always be eaten by it
and it should also always have that same symbol
where it's getting bigger or smaller.
And then 3 is equal to 3.
If they have the same location
on a number line, then they are equal.
So that is true.
All right.
So here's what I want.
I want you to put the inequality that matches for each of these
and yes, there are some simplifying here.
So if you have not done the opposite
in absolute value basically the introduction to integers,
please watch that video first unless you already know how
to do it.
But here are six problems for you to try.
So I want you to hit pause and try them.
Remember, if you need a number line, draw a number line.
Anything that helps you.
Pictures whatever.
Never be afraid or ashamed to use them.
So hit pause now.
And these are your answers.
So if you drew a little line, you could see that 7 is bigger
than 5 so you should make sure that it eats the 7.
Negative 7 is less than 5, so 5 is bigger.
It should eat the 5.
Negative 6 and negative 17
so even though 17 is a larger number than 6,
negatives are opposite directions
so the more negative you get the more money you owe
so basically you're worse off than the person who only owes 6.
Right? So it's negative 6 is better.
It's bigger.
And then when you have these where they're not simplified,
you have to simplify them.
So absolute value of negative 5 is 5,
5 is bigger than negative 5.
Remember, this is the opposite of that so if you just cover it,
you get 5, now it's negative 5.
Cover it you get 6, now it's negative 6
and this is opposite of negative 6.
So remember opposite of a positive 5 is negative 5.
Opposite of a positive 6 not negative is negative 6
and opposite of a positive 5 is negative 5.
All right.
Thank you.