Inequalities | Algebra | Maths | FuseSchool

An equal’s sign means two expressions are equal to one another. But sometimes the expressions are not equal… we might only know that something is bigger than or smaller than something else… this is where inequalities come into play. Things that are not equal, hence the word inequalities! In this video we are going to look at the basics of inequalities - the different symbols and how they are represented on number lines. 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 4. It means that a can be 4, 5, 6 and any number bigger. On a number line, it would look like this... See how it is represented with a full circle... Whereas b is less than 2 is 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. There’s a closed circle here, so the value is going to be greater than or equal to minus 2 And a hollow circle here. So, it’s going to be less than 4. 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 2 is less than or equal to x which is less than 4”.