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### Course: Algebra (all content) > Unit 2

Lesson 13: Introduction to inequalities with variables# Plotting inequalities

To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in. Finally, draw a line going from the circle in the direction of the numbers that make the inequality true. Created by Sal Khan.

## Want to join the conversation?

- At1:52can we also use <= instead of ≤ ? Will that be correct?(24 votes)
- If you are writing the symbol by hand, then you should use "≤". When typing on a keyboard, it is common to use "<=" as it requires no special characters other than what is already on the keyboard.

In KhanAcademy exercises, they provide a menu of special symbols so that you can use "≤".(29 votes)

- Hi,

Small question, I just want to know how can I get the most out of these lectures on Khan academy. Any tip or tricks welcome here ;).

Thanks(11 votes)- Pause the video and have a go at the question. This will make you think and help better understand the problem. Also, you can identify any mistakes you might have made and correct them.

Do all the exercises, try to get 100%. It's okay even if you don't, the goal here is to practice and learn.

Take notes, jot down anything you feel is helpful. (I like to summarize each topic to one page so I can quickly go through everything.)

Don't give up if you don't understand something. Take a short break, maybe listen to some music. Come back and try again.

If you are stuck, you can also ask for help in the comments section.

This article has more ideas: https://www.khanacademy.org/khan-for-educators/resources/students/resources-for-students/a/seven-tips-for-making-the-most-out-of-khan-academy

Good luck!(26 votes)

- When graphing less than or less than and equal to 1500 calories/day, you shade the number line in so that it goes below zero into the negative. How can you consume a negative number of calories in a day?(9 votes)
- Of course, to consume negative calories you would not be gaining any calories, but losing them. Meaning you would be working out and burning them.

To answer your first question, he shaded the arrow at zero which shows it can be any negative number beyond zero as well. So we displayed that on the number line.(3 votes)

- When will Khan academy add learning games to make the person watching more fun.(4 votes)
- You can code your own learning game on KA.

Check it out here:

https://www.khanacademy.org/computing/computer-programming

But for now, there isn't any games provided by official KA for us to learn, so you may have to check out programs made by other learners.

For example, here's one from myself:

https://www.khanacademy.org/computer-programming/single-variable-compound-inequalities-plotter-number-lines/6342204304572416

Not exactly a game but it's still kinda interactive?(3 votes)

- Wait, so for all of the number lines, should there be a minimal amount of 0 whatever?(4 votes)
- Not necessarily. For some and actually many number lines, zero is not the least number. It really just depends on the problem. If negative numbers can be included with the problem still being valid, it is not logical for zero to be the least number of value.(1 vote)

- i do have a question(3 votes)
- I have a challenge for all Khan academy learners;

Mr. Monroe keeps a bag of small prizes to distribute to his students. He likes to keep at least twice as many prizes in the bag as he has students. The bag currently has 79 prices in it. Mr. Monroe has 117 students. How many more prizes does he need to buy.

Write the answer as a comment in an Inequality equation

For example 5000<=83x+850(4 votes)- Prizes = p

Needs: 117*2p prizes.

Has: 79 prizes.

Will buy: 234p - 79p = 155 prizes.

He likes to keep**atleast**double the amount of prizes as students. Thus, our equation is:`p≥155`

(Did I do it right? 🤔)(0 votes)

- Why is the less than sign is pointed to 1500 at1:00?(3 votes)
- I really enjoy watching this(3 votes)
- That's nice. You could put that in the tips and thanks post to share your feedback more effectively.(1 vote)

- not a question just wanted to say hi(3 votes)

## Video transcript

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.