Now we're going to learn how to write inequalities from graphs. And the inequalities that we're going to see in this lesson are going to be set up on number lines. When we look at the number line, there's three very important things that we need to look for. First, what number has a circle with it? Second, is that circle open or closed? A closed circle just means that it's colored in. And third, which part of the number line is shaded? Once we figure out those three pieces of information, we'll know exactly what inequality symbol to use when we set up our answer. And just to review, and this is important for us to know our four inequality symbols, we have greater than, less than, greater than, or equal to, and less than or equal to. So all of our answers are going to have one of these four symbols with it. Let's look at an example. Write an inequality to represent the graph. So we can see here that part of our number line is represented with this blue arrow. We also have a circle with the number two. Everything that we see that's in blue represents the solutions to our inequality. So we don't have a variable provided for us, so we can make up some variable to represent all of the solutions that we see here in blue. Let's just use the variable x. So x can be all of those numbers that are to the left of two. We can see that we have our open circle at positive two, and everything to the left is shaded in blue. So x can be negative five, negative one, it could be zero, it could be positive one. And notice that all the way to the left, the arrow part of our number line is also shaded in blue. So that means that our solutions for x keep going on and on to infinity as we go further into the negative numbers to the left. So now that we look for our circle, which we see at the number two, it's an open circle and our number line is shaded to the left of two. Now let's see what all of that information tells us to help us represent our inequality. First, the open circle at two tells us that x is not equal to two. Two is not included as part of the solution set for x, anything less than two is included. So we could say 1.99 is a part of our solution set for x, but not exactly two. And we can see that since our number line is shaded to the left of two. So that tells us that x can be anything less than two. So we know that x can be anything less than two, but not exactly equal to two. So the best symbol for us to use is the less than symbol. So our inequality says that x is less than two. Let's look at one more example. So we're going to look for those same three pieces of information. We want to see what number has the circle with it, whether the circle is opened or closed, and which direction the number line is shaded. So we can see that we have a closed circle at the number negative three, and everything to the right of that is shaded in, including the arrow at the end of the number line. So that tells us that all these solutions for this inequality keep going on and on for infinity in that positive direction to the right. So we'll need to pick a variable to represent these solutions that are colored in blue. We can use x again, or you can make up whatever letter variable you want. And since this time we have a closed circle at negative three, that means that x is equal to negative three. The closed circle means that we include that number as one of the solutions for x. So this time x can be equal to negative three. And since everything to the right on that number line is shaded, then x is greater than negative three. So now we see the x is greater than negative three, but also equal to negative three because the circle is shaded in. Putting that together tells us that the best symbol to use is the greater than or equal sign. So x is greater than or equal to negative three. So just remember, ask yourself those three questions and that will help you to figure out exactly how to set up your inequality from a graph.