in this video we're going to cover how to solve inequalities like these three the idea is exactly the same as when we're solving normal equations with an equal sign so just like how we normally won't see the unknown letter by itself on one side of the equation and that's exactly what we're trying to do here as well so in this first inequality x plus three is less than eight to get the x on the left by itself we're gonna have to subtract three from both sides to find that x is less than five and that's it so essentially we treat the inequality sign as if it's an equal sign but we don't actually change it to an equal sign the only important difference they need to know about is that if you multiply or divide both sides by a negative number then you have to swap the inequality sign around for example in this second equation to get rid of the divide by negative two part we need to multiply both sides by negative 2 which will leave us with just the x on the left and negative 10 on the right but importantly because we multiplied by a negative number we're gonna have to swap our inequality sign around so that it will change from a less than to a more than sign which leaves us with x is more than negative 10. the last question here 7 plus 2x is more than or equal to 13 is a bit trickier because it involves two steps the first thing we're gonna have to do is take away seven from both sides to get two x is more than or equal to six and then we have to divide both sides by two to get x is more than or equal to three and that's it let's try a couple more for this first one there are two different ways that you could do it one is to subtract 5 from both sides to get minus 3x is less than or equal to negative 15. and then divide both sides by negative three to find that x is more than or equal to five and if you didn't notice we swapped our inequality sign around here because we were dividing by a negative number then the second way that we could have done this question would be to add 3x to both sides to get 5 is less than or equal to negative 10 plus 3x then add 10 to both sides to get 15 is less than or equal to 3x and finally divide both sides by 3 to get 5 is less than or equal to x and remember this is exactly the same thing as saying that x is more than or equal to 5 like we got in the first place in situations like this it doesn't really matter which way round you do it just go with whichever one you feel most comfortable with or whichever one you think of at the time for the second question there are also two ways of doing it because we could try to put the x's on the left or the right but because at the moment there are more x's on the left hand side it'll be better to keep our x's on the left and put our numbers on the right so the first thing you do is subtract x from both sides to get three x plus seven is more than negative four then you can subtract seven from both sides to get three x is more than negative eleven and finally divide both sides by 3 to get x is more than negative 11 over 3 and we can leave our answer like that because we can't simplify negative 11 over 3. anyway that's everything for this video so hope that all made sense if you enjoyed it then do give us a like and subscribe and cheers for watching you