In this video, we're going to look at the different ways that we can write inequalities. So here we have x is greater than zero. And notice that our variable x is on the left side. This is the most common way to write it. So we normally do put the variable on the left side of the inequality, but you don't have have to. There is another way to write it. Let's look further into this inequality and what it actually represents, and then we'll look at the other way that we can write it. So we know that this inequality reads as x is greater than zero. And if we represent this on a number line, we can see that x is everything shaded in blue, all of the numbers that are greater than zero, everything that's to the right of zero on the number line. But we could also look at this as zero is less than all of the values in blue that represent x. So we could also say that zero is less than x. And look at both of the ways that we wrote this inequality. They look very different. The one at the top has x on the left hand side and our number on the right hand side. And the one below, we have it flipped. Zero is on the left and x is on the right. But they both represent the same set of values for x. So if you do decide that you want to flip your inequality around, make sure that you also flip the symbol around. So it's okay to write it the other way, but just remember to flip that symbol for the inequality as well. Here's another way to think of it. If we look at these two boys and we want to compare their heights, we could say that Kyle is taller than Devon, but we could also say that Devon is shorter than Kyle. So we're comparing their heights but using two sets of wording that's different. In the first sentence, we have Kyle first, and then we're comparing it to Devon. In the second sentence, we have Devon first, and then we're comparing his height to Kyle. So notice we switched their names around, we switched the placement, and when we did that, we also had to switch the word that we used to compare it. First, we use the word taller when we compared Kyle to Devon, and then we use the word shorter when we compared Devon to Kyle. So when we switched the order of their names, we had to use the opposite comparison word in the sentence. And it's the same thing with inequalities. When we switched the order of the inequality, we had to switch the inequality to the opposite side. So let's look at how that works when we're actually solving an inequality. So here we have x plus five is less than or equal to eight. Now, if we want to write this inequality the other way we can flip it so that eight is on the left hand side. So we have eight is greater or equal to x plus five. So now we have x plus five on the right side. And notice that we did flip the inequality symbol around as well. Now we're going to go ahead and solve these inequalities and when we solve it, our solutions to still represent the same values of x and we're going to look at it on a number line just to make sure that it works. So here we go, let's solve the one on the left first. So to get x by itself, we're going to subtract five from both sides. And now we're left with x is less than or equal to three. Now the one on the right hand side, we also will subtract five from both sides to get x by itself. And now we have three is greater than or equal to x. So now let's look at our solutions. We have the same numbers, we have three, we have the same variables, we have x in both cases, but they're flipped around and we also have the inequality symbols that are flipped around. But if we graph this solution, it will look like this. We still have everything in blue representing our solutions for x. So x is everything less than or equal to three because it includes three and everything to the left of three. But we can also say that three is greater than or equal to x based on the way that we have the set second inequality problem written. So they both represent the same solutions for x though, even though they're written in different ways.