 An equal sign means that two expressions are equal to one another. However, expressions might not always be equal. We might only know that one thing is bigger or smaller than another thing. This is where inequalities come into play. Two things are not equal, hence the word inequality. In this video, we're going to look at the basics of inequalities, the symbols that are used and how they look on a number line. Inequalities are really useful when looking at profits and losses, for example, or for loans, or for working out anything that may have a range of values, like when to photograph a diver jumping off a diving board. These are the symbols for inequalities. A is less than B. The small side is next to A, and the big open mouth is next to B. So A is smaller than B. A is bigger than B. A has the big side this time. A is less than or equal to B. The line underneath means or equal to. A is more than or equal to B. If we had this inequality, A is bigger than or equal to four. It means that A can be four, five, six, and any number that's bigger. On a number line, it would look like this. See how it's represented with a full circle, whereas B is less than two. It's a hollow circle on a number line. An easy way to remember is to think that the full circle also includes or equal to. Hence, it is complete. It includes everything. The hollow circle is just more than or less than. It's missing the or equal to, and so is hollow. When inequalities are shown for these number lines, pause the video, work it out, click play when you're ready. Did you get them right? Can you work out the inequality for this one? Pause the video and have a think. There's a closed circle here, so the value is going to be greater than or equal to minus two. And a hollow circle here, so it's going to be less than four. We can combine these things into a double inequality, which we would write like this. Notice how we put X in the middle, so it appears just once. If we read this double inequality out loud, it says minus two is less than or equal to X, which is less than four. Here's some questions for you to do. Pause the video, answer them and click play when you're ready. How did you get on? So that's our introduction to inequalities finished. We're going to look at how to solve inequalities and how to plot them on a graph in different videos. If you liked the video, give it a thumbs up and don't forget to subscribe, comment below if you have any questions. Why not check out our Fuse school app as well? Until next time.