In our last few lessons, we've been working on equations and how to solve them. Now we're going to learn about inequalities. We're going to look at the differences between equations and inequalities, and we'll also learn the symbols that are used in inequalities. So first, what's the difference between an equation and an inequality? Well, with equations, there's the same value on each side of that equation. And we can recognize equations because they have an equal sign. So if we look at this example, it says 52 equals 52. We see the equal sign in the middle and we see that both sides of that equal sign have the same value. In this case, 52. This also represents an equation. We see the equal sign, and even though the left side says 50 plus two, that still has a value of 52. So both sides of this equation still have a value of 52, even though they're written differently. We can also see variables in our equations. This equation says x equals 52. So it's really telling us that x is 52. Inequalities, on the other hand, may have a different value on each side. One side might have a value that's more or less than the other side of that inequality. And instead of an equal sign, they will have an inequality sign. And there's four different types of inequality signs that we're going to look at in this lesson. Here's an example. We have 20 and we'll soon learn that the symbol in the middle represents greater than and then a seven on the other side. Now we can see that we have an inequality symbol in the middle. It's definitely not an equal sign. And we have two different values on each side. 20 and 7 are definitely not the same value. And this is another example of an inequality. On the left side, it's written as two times ten instead of just 20, but it still represents 20. And the other side is a seven. Still different values. Or we could represent it with some variable. In this example, it's saying that x is greater than seven. We don't know exactly what value x represents, but it's something that's greater or more than seven. Okay, so more about that greater than symbol, we can see that it almost looks like an arrow. On the left side we're going to have the bigger value, and on the right side we'll have the smaller value. Just like in that previous example we had, 20 was greater than seven to 20, which was bigger was on the left side, and the seven, which is smaller, was on the right side. You can also think of it as the arrow points towards the smaller value. If we use a variable, we could say x is greater than five, and that's just how we would read it in words. X is greater than five. X could be six, seven, it could be 101,000. It could be any number that's more than five. Next we have the less than symbol. Notice that now the symbol is pointing the other way, it's pointing to the left. Well, on the left side of this we'll have the smaller value. Remember, think of it as the arrow pointing towards the smaller value and on the right side we'll see the bigger value. So if we say x is less than five, then x could be any number that is smaller than five. It could be four, it could be zero, it could be negative 10,000, it could be any number that is smaller than five. And here we have greater than or equal to. So notice that there's two parts to this symbol. The top part looks like the greater than sign that we just learned. And then the bottom part looks like one of the lines of an equal sign. And it is just like both symbols being put together to represent greater than or equal to. So if we look at this example, we would read it as x is greater than or equal to five. So even though we don't know exactly what number x is, x could be equal to five, or it could also be any number greater than five. So there's really an infinite number of values that x could represent. And that's what we'll see with all inequalities. The variable can represent an infinite number of values. Now we have less than or equal to the top part of the symbol, we have the less than symbol and then we have the line that represents the equal to part. So we would read this as x is less than or equal to five. So once again x could be equal to five, or it could be any number that is smaller than five. So here's all four inequality symbols written together. This is definitely something that you want to remember and have written down so that when you see this in different types of problems, you'll know just what that symbol represents.