Graphing Inequalities on Number Lines Math with Mr J

Welcome to math with Mr. In this video, I'm going to cover how to graph inequalities on number lines. Now, when we graph inequalities on number lines, this really helps us visualize what inequalities mean and gives us better overall understanding of inequalities. We'll go through four examples together here in order to get this down. Now, at the top of the screen, there are two very important notes that will help us with graphing these inequalities on number lines. So, if we use filled circle, the number is included. If we use an open circle, the number is not included. And you'll see exactly what that means as we go through our examples. So, let's jump into number one where we have is less than three. So, our variable here has to have value less than three. Now, this is not less than or equal to symbol, so we want an open circle because three is not included. So, we're going to put an open circle on three. And again, that indicates that we are not including three in our solutions. Now, is less than three, so any number less than three is going to be correct solution. So, we draw an arrow pointing in the direction of the numbers less than three. This is going to represent all of the solutions that will work for this inequality. So, let's draw an arrow to the left here and include all of the values less than three. So, for example, if we were to say equals zero, right here, equals zero, zero is less than three. That would be solution. So on and so forth for all of those values less than three. We have an infinite amount of solutions, and that's what that arrow represents. And again, we used an open circle because three is not included in our solutions. So, let's move on to number two where we have -2 is less than or equal to So, for number two, anything greater than or equal to -2 would be solution. So, what we can do, let's start at -2, and this is filled circle because -2 is included because we have an or equal to symbol. So, let's fill in our circle here. Now, can be anything greater than or equal to -2. So, we want all the values that are greater than this to be represented. So, we need our arrow pointing to the right here, and that indicates everything greater than -2 is going to be solution. So, for example, let's just pick out four. And if we were to plug in four, -2 is less than or equal to four, well, that would be solution. That would be correct. So, that arrow represents all of the numbers greater than -2, and then our filled circle right here represents -2 being included in our solutions because again, we had an or equal to symbol. On to number three where we have is greater than or equal to 57. So, this is another one that we have or equal to. So, any value greater than or equal to 57 would be solution. So, we need filled circle including 57, and then we want all the values that are greater than 57 to be represented, and that's going to be our arrow here. So, for example, 60 would be solution. 60 is greater than or equal to 57. So, the arrow represents all values greater than 57, and the filled circle represents 57 being included in our solutions. So, let's move on to number four where we have 14 is greater than So, 14 is not included in the solutions here because we do not have an or equal to symbol. We just have greater than symbol. So, we're going to use an open circle because we do not want to include 14. Now, correct solutions are going to be any numbers less than 14. So, we're going to represent that with an arrow pointing in the direction of all the numbers less than 14. So, for example, if we were to say that equals 13, would that be correct solution? Well, 14 is greater than 13. Yes, that is correct. And we have an infinite amount of solutions, so that arrow represents all of those solutions that are less than 14. And again, an open circle because 14 is not included in the solutions. So, there you have it. There's how you graph inequalities on number lines. hope that helped. Thanks so much for watching. Until next time, peace.