in this example, we're being asked to graph the following inequalities on the number line. So let's take a look at number one. It says that three is less than or equal to X. So remember, the first thing we want to do is to determine whether you should have an open circle or close circle it. Three. Well, that would mean is three a solution to our inequality? Well, is three less than or equal to three? Well, yes, it ISS because three is less than or equal to three because it is equal to it. So that tells us we're going to have a close circle at three under number line. So now we just have to determine, should we shade the values to the left or to the right of three. Now, this could be a little tricky when the X is written second, so my hint. Sometimes it's always to flip it around. So let's think about if I was to take our original inequality. Three is less than equal to X and switched around, so X was first. So, in other words, I'm going to rewrite it so that X is first and the three a second. Here's where we're gonna be careful. Notice how the mouth of our inequality is facing the X. What? When we flip it around, it still has to be facing it, so it's going to become a greater than or equal to sign. So know this when we flip it around. The inequalities sign also flips. So now take a look at her inequality. It says that X has to be greater than or equal to three, meaning we need to shade all the values of X that are larger than three wolf. They're larger than three. They should happen to the right of three. So on our number line, we're going to shade to the right because all of these values of X will be greater than three and will make our inequality true. Now let's go ahead and take a look at number four are sorry. Number two. It says that negative four is greater than X again. The first thing we need to determine it. Should we have an open or closed circle? Well, is negative four greater than negative four? Well, this would be a false statement. Negative four is not greater than negative for their equal to each other. That means negative four is not a solution. So that negative for in their number line, We're going to have an open circle. So now we have to determine should our solutions for X B to the left or to the right of our circle. Now, just as in the previous search, our example, it's a little bit harder when you're variable is not first. So my recommendation is we're going to take our inequality sign, and we're gonna flip it around just as we did before. So we're gonna have XP first and negative 42nd. But notice in our original problem that the arrow is pointing towards the ex. So when we rewrite this, we're gonna flip it around because the arrow should still be pointing to the X. So now take a look at our inequality. It says that X is less than negative four. Well, our values of X that are less than negative four to the left or to the right. Well, that would be to the left. So now we know that we're going to shade on our number line All the values of X that are less than negative four, meaning we're going to shade to the left. So my recommendation and you don't have to take it is that when you have your inequalities, especially will be true when you're solving inequalities is if you're variable is on the right, so flip your inequality around, so that way you'll be to the left A lot of time that's easier to determine. Should be shade to the left it to the right. But don't forget. When you do that, you're gonna also have to flip the inequality sign around. Justus. We didn't notice the value didn't change. Just the inequality changed.