 As a general rule, inequalities are more important than equalities. You'd rather pay less than $100 for an item than exactly $100. Or you'd hope to get at least 90% on an exam rather than exactly 90%. Or you've planned that a project will take no more than two weeks to complete, and you don't want it to take exactly two weeks. It's useful to be able to move back and forth between algebra and geometry. Algebra is all about numbers and formulas and equations. Geometry is about pictures. And, as the saying goes, a picture is worth a thousand words. So it's helpful to draw a picture of an inequality on a number line, and we'll do so as follows. First, we'll identify the boundaries of the inequality. And since inequalities come in two flavors, depending on whether we include or exclude the endpoint, we'll use a closed circle to indicate a boundary is included, and we'll use an open circle to indicate a boundary is excluded. And then once we've indicated the boundaries, we'll shade the portion of the number line that corresponds to the inequality. For example, suppose I want to graph the inequality x greater than 5. Now the inequality describes all numbers greater than 5, so 5 is a boundary. So let's put down our number line. Since the inequality is strict, we're not allowed to actually equal 5, we exclude 5 and represent it using an open circle. Since we want to include all numbers greater than 5, we shade the portion of the number line that includes these greater numbers. So we shade the part of the number line to the right of 5. If that's just one problem, where do we stop? In fact, we can never stop because we want everything that's greater than 5. But we only have a finite amount of paper, so instead of going to the right forever, we'll use an arrow to indicate that we never stop going to the right. Or how about the inequality x less than or equal to negative 3? So we'll throw down our number line. And since negative 3 is a boundary and our inequality allows us to be equal to negative 3, we'll use a closed circle. Since our inequality is x less than or equal to negative 3, we want everything less than negative 3, so we shade to the left. And we want to use an arrow to indicate that we never stop shading to the left. We should also be able to go backwards. So we want to be able to take a graph like this and express it as an inequality. So first, we see that negative 2 is a boundary, but it's excluded because it has an open circle. Next, we see that the shaded portion includes everything less than negative 2. So this corresponds to the inequality x is less than negative 2.