in this video we're going to cover the basics of inequalities so we'll take a look at what all the different symbols mean and also how to represent inequalities on a number line let's start with the symbols if we look at this expression it means that x is less than 10. so x could be 9 or 8 or three or negative four basically anything that's less than ten whereas if we had this expression this one means that x is more than ten so a number like 11 12 50 or 200. the thing that students normally find hardest about this topic though is just remembering which symbols which so one way that might help you remember it is remember that the less than sign looks a little bit like an l so l for less than and if you can remember that then you know that the other sign which doesn't look like an l must be the more than sign the next thing we need to look at are these two symbols which look pretty much the same as our less than and more than signs except they also have these horizontal lines underneath them the straight lines basically mean or equal to so this first expression means that x is less than or equal to 10. so as well as being numbers like 9 8 3 or negative 4 x could also be 10 itself similarly the second expression means that x is more than or equal to so again the number might be ten itself or any number bigger than ten another important thing to know is that when we take an expression like x is less than ten that means exactly the same thing as 10 is more than x in both cases we're saying that 10 is the bigger value and x is a smaller value we can also use negative numbers with inequalities for example x is less than a negative five means that x can be any value smaller than negative five for example negative 5.5 negative 17 negative 100 and so on whereas if x was bigger than or equal to negative 5 then it could be negative 5 itself or anything bigger like negative 2 positive 2 or positive 50. the last thing we need to cover are inequalities like this which contain more than one inequality sign the signs work in exactly the same way though so this one just means that 3 is less than x and that x is less than or equal to 7. or in other words x has to be between three and seven so if we were told that x is a whole number then x must be four five six or seven because remember it can't be 3 itself because 3 is less than x but it can be 7 itself you also need to understand how to represent these inequalities on number lines so for this one if we look at this number line of 0 to 10 x must be somewhere in this region between 3 and 7. so we put little circles above the three and the seven the important bit though is that because x can also be equal to seven itself we need to color in this circle on the right which tells us that x can be seven whereas because x can't be three we leave the circle above three empty let's have a go at one more so for this question we need to show the inequality negative three is less than or equal to x which is less than four on a number line so if we draw a number line from minus five to positive five then we can put little circles above the minus three and the four and join them up with a line then the last thing we need to do is check if we need to fill in either of our circles so because it says that negative 3 is less than or equal to x we know that x can be negative three itself and so we have to fill in the circle above the negative three whereas because x has to be less than four we know that x can't be four itself and so we leave the circle above the four empty anyway that's everything for this video so hope that all made sense if it did then please do give us a like and subscribe and cheers for watching