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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.

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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.