I’m starting to take a little

bit more care of my health, and I start counting

my actual calories. And let’s say C is equal

to the number of calories I eat in a given day. And I want to lose some weight. So, in particular, I want to

eat less than 1,500 calories in a day. So how can I express

that as an inequality? Well, I want the number

of calories in a day to be less than– and

remember, the less than symbol, I make it point to

the smaller thing. So I want the calories

to be less than 1,500. So this is one way

of expressing it. I say, look, the

number of calories that I consume in a day

need to be less than 1,500. Now, one thing to

keep in mind when I write that is obviously if

I eat no calories in a day, or if I eat 100 calories,

or if I eat 1,400 calories, or if I eat 1,499 calories for

C, those are all legitimate. Those are all less than 1,500. But what about 1,500 calories? Is it true that 1,500

is less than 1,500? No. 1,500 is equal to 1,500. So this is not a true statement. But what if I want to eat up to

and including 1,500 calories? I want to make sure that I

get every calorie in there. How can I express that? How can express that

I can eat less than or equal to 1,500 calories,

so I can eat up to and including 1,500 calories? Right now, this is only up

to but not including 1,500. How could I express that? Well, the way I would do that

is to throw this little line under the less than sign. Now, this is not just less than. This is less than or equal to. So this symbol right

over here, this is saying that C is less than

or equal to 1,500 calories. So now 1,500 would be

a completely legitimate C, a completely

legitimate number of calories to have in a day. And if we wanted to visualize

this on a number line, the way we would

think about it, let’s say that this right over

here is our number line. I’m not going to count all

the way from 0 to 1,500, but let’s imagine that

this right over here is 0. Let’s say this

over here is 1,500. How would we display less

than or equal to 1,500 a number line? Well, we would say,

look, we could be 1,500, so we’ll put a little solid

circle right over there. And then we can be less

than it, so then we would color in everything

less than 1,500, and say, look, anything

less than or equal to 1,500 is legitimate. And you might say, hey, but

what about the situation where it wasn’t less than or equal? What about the situation

if it was just less than? So let me draw that, too. So going back to

where we started, if I were to say C

is less than 1,500, the way we would depict that

on a number line is– let’s say this is 0, this is 1,500,

we want to make it very clear that we’re not including

the value 1,500. So we would put an

open circle around it. Notice, if we’re including

1,500, we fill in the circle. If we’re not including 1,500,

so we’re only less than, we were very explicit that

we don’t color in the circle. But then we show that, look, we

can do everything below that. Now, you’re probably saying,

OK, Sal, you did less than, you did less than or

equal, what if you wanted to do it the

other way around? What if you wanted to do greater

than and greater than or equal? Well, let’s think about

that for a second. Let’s say that I’m

also trying to increase the amount of water I intake. And so let’s define

some variable. Let’s say W is equal to the

number of ounces of water I consume per day. And I’ve read that I

should have at least– let me throw out a number– 64

ounces of water per day. There’s one way I could

think about, where I always want to drink more

than 64 ounces, so that would be W

is greater than 64. W here is the thing that

I want to be bigger, so the opening is to the W.

W is greater than 64 ounces. How would I depict that? Well, let me do my number

line right over here. Let’s say that this is 0. This is 64. If I wanted to make

strictly greater than, so in this situation it’s not cool

if I just drink exactly 64. That 64 is not greater than 64. I have to drink 64.01

ounces or 0.00001 ounces. It has to be something

that is greater than 64. So I’m not going to include

64, but anything greater than that is completely cool. Now, what if I want to

loosen things a little bit? It’s OK if I drink

exactly 64 ounces or more. Well, then I could write W is

greater than or equal to 64. And the way that I would be

depict that on the number line– and obviously, I’m

not showing all the numbers in between– let’s

say this is 0, and then we go all

the way up to 64. Well, now it’s OK if I

drink exactly 64 ounces, so I’m going to fill

in the circle now. Here I opened it because

64 was not a cool number. Now, 64 is completely OK. I can drink exactly 64 ounces

of water in the day or more, and then I just go up the

number line just like that.

Since we was talking bout anyqualities i wanna point out justice system got dat inequality my nigga trayvon in heaven and george zimmerman a freeman… smh….

I think instead of saying "I point the less than symbol to the lesser number" you should clarify that the symbol itself is saying that the left is smaller. The symbol is clearly showing what is bigger and what is smaller, the point at the end is not relevant, idk, it's just me, but then again, I wasn't stupid

I think it depends on how you look at it

5>2

2<5

Is the same

lol, atleast throw some math in there: Trayvoyn < Zinnerman

Thanks, Yeah, one says 5 is bigger than 2 the other says 2 is smaller than 5. It's the same, but it's important to realize why the sign is what it is, describing it as an arrow that points to the smaller number or value is what I am not comfortable with. Just like I am uncomfortable when people teach calculating the area of a triangle without saying that it's just half of a rectangular.

Jny

I never new I would be learning again! I love you Salmon Khan, and look forward to some computer science next! I now know what those symbols, and how the work on a gragh or line. Inequalities and equalities and equal to or true or false statements work on a line.

That's what I just said.

thanks

How would you graph x does not equal -5 on a number line?

Khan Academy is a lifesaver,especially for homeschooled kids.

This is PRE-ALGEBRA on the Khan Academy site… I would say PRE-SCHOOL everywhere else in the world. Like or Comment this if you're reading this on 2015

I am trying to do some 6th grade math, and we're looking at " I can solve an inequality for a variable and graph the solution set on a number line", do you have any videos for that stuff?

Idk if this is right but, I had one that was greater than and I did this <-0-

~~————7~~> With a closed circle. I hope it is right..C < 1500 would mean C is greater than 1500 so it would be C > 1500…

thx kan

Pls Sir solve this for me.

|x| -1/|x| -2 ≥ 0. x € R, x ≠ ±2.

nice

im a homeschool kid

I️ am a fourth grader watching this

Thanks chief

why can't teachers explain it like this. they make it so complex

My teacher told me put the arrow the way the variable is facing is this correct?

Dang this helped me a lot thank u

the first one is wrong why did you draw the yellow colour line after 0

Let's all take a moment to thank this man (and other Khan teachers) for providing clear explanations and providing aid to students who might not get things the first time around.

If I didnt have this video I probably would of failed this unit thx

been using since 3rd grade nice job