 Now one thing you should keep in mind when it comes to the equal sign, when you're simplifying things, you can have terms where there's only numbers involved. So you can have 2 plus 5. So 2 plus 5 is 7. We already know that. And that's simplified. When it comes to the equal sign, you're going to have to have at least one variable. And a variable is usually a symbol or a letter. Usually we use letters for variables. You're going to have a variable in there where you're trying to solve for something. So there has to be an unknown, or initially anyway for us, there's going to be an unknown in our equations. When we start doing this. So we're going to have x is equal to 5. So there's going to be a letter in the symbol. Keep this in mind. The first operations that we learned when we started the language of mathematics was how to add and subtract. So let's see how additional subtraction work together with the equal sign. Let's start off with basics. Let's go x plus 5 is equal to... Now what we do when you have addition and equal sign. What this is, is two terms on the left side and one term on the right side. Whenever you have additional subtraction, that's your separation of terms. Unless they're all divided by something. But we'll get into that detail. Let's just talk about this for now. How we solve for x and we're solving for something. What it means is we're getting the letter on one side of the equation by itself. So whenever they say solve for something, what you have to do is get that letter by itself on one side of the equation. And the letter we refer to as a variable. The way the equal sign works is if you want to get rid of something on one side of the equation, you have to do the opposite to it from that side. And because this is an equal sign, you have to balance things out. If you do something on one side of the equation, you have to do it to the other side of the equation. So what we do here is this is x plus 5 is equal to 2. What we want to do is get x by itself. So we have to get rid of the 5. What we're going to do is that's plus 5. We're going to subtract 5. So we're going to go minus 5 on this side. And because we have an equal sign and the equal sign means we have to balance things out, whatever we do on one side, we've got to do to the other side. So if we subtract 5 from this side, we have to subtract 5 from the other side. Minus 5. So this guy kills this guy, right? All we've got left on this side is just an x. So x equals 2. 2 minus 5 is negative 3. And that's your answer. x is equal to negative 3. One tip that you should keep, you know, use, or one way to lay all this stuff out is math is very visual. So what I like doing, personally it helps me out a lot, is I line up my equal sign whenever I'm solving for things. You know, try to get some kind of balance happening. And what happens is usually if you have a large equation, if you're balancing your equal sign down the middle, your equation gets smaller and smaller. You end up with a, you know, triangle, backwards triangle, an upside down triangle or a cone or something like that. So it looks quite nice, okay? It looks pretty cool. If you do it, you know, hopefully it works out that way. Sometimes you introduce new things and the equation, it blows up. It becomes crazy. But in general, just the simple stuff, you start off with, you know, certain term on one side, certain term on the other side, your equal sign in the middle, line up your equal sign and start crunching things around and what you notice, you end up with a V. Okay? Let's go deal with the minus sign. The minus sign works the same way. So I'm going to make the next question a little bit more complicated than this one. Let's look at the minus sign, right? For the minus sign, let's add a couple more, well, the same variable in there because when you're solving for something in general, you only have one variable, one type of letter in the equation initially. Later on, we're going to deal with a lot more variables and that's really getting into functions, okay? That's precursor to functions and we'll deal with some of that stuff later on. I added a plus sign and a minus sign. What we do with these types of problems, we have an X on one side of the equation and an X on the other side of the equation, right? What we have to do when we're solving, when they say solve for this kind of thing, we have to get all the letters to one side and the numbers to the other side and initially there's only going to be one letter, one variable. So what you have to do is get the variable to one side and everything else to the other side. So let's start moving things around. Again, if you want to get rid of plus five over here, you move it to the other side. But what you should always do is simplify before you start moving things around. If you can simplify one side of the equation and simplify another side of the equation, then do that because that reduces the number of steps you have to do, okay? So let's simplify this for now. X plus five minus three. We can't combine these because they're not, you know, the same term, but we can definitely add these. The sign, as we said before in the first series, I think, the sign in front of the number always goes with the number, right? So that's a positive five minus three that gives you two. So this side, you know, you can cross this out because it's plus two, right? So now you've got X plus two is equal to two X minus one. What we want to do is bring the two X over, take the two over there, right? Now instead of doing, you know, subtracting two on this side and subtracting two X on this side, what I like doing is circling them and moving them. Visually, it just makes sense to me. For some reason it just makes sense to me. And whenever I do that, what it tells me to do is change the sign of the number. So what I do is grab this guy and say this guy has to come over here and that's plus two so that they come to minus two. And this guy, I have to grab and bring it over here because we would normally just go minus two X. What I'm going to do is just go, comes over and this tells me as soon as I jump over an equal sign it changes the sign. This was positive two X and it becomes negative two X. Now this may look complicated, this is messy, but when you start doing these things, the more you do the simpler it becomes basically. And you can deal with a huge problem. Hopefully we'll later on go to a gigantic one and I'll make a huge problem and we'll go through it and we'll draw all these things. But let's continue with this thing. What you've got here is negative two X and that's a positive X. So negative two X plus X is negative X. Line up your equal sign. Negative X is equal to, that's negative one minus two. Negative one minus two is negative three. So you've got negative X is equal to negative three. There's two ways to continue this because you're not just looking to get, you know, negative X to one side. You need to get X to one side. The variable has to be completely isolated. No negative numbers, most square root symbols. That's what it means when they say solve for something. It means the letter, the variable, has to be completely isolated on one side and everything else on the other side. Now over here, we haven't isolated yet. This is negative X is equal to negative three. Right now, we're just dealing with additional subtraction, moving things around. Later on, when we do division, all you have to do is divide one side of the equation by negative one and divide the other side of the equation by negative one and negative signs disappear. We'll multiply both sides of the equation by negative one. What we're going to do right now, because we're just dealing with addition and subtraction, we're just going to move them, move this guy to the other side. So let's do this with a different color pencil, it shows. So we're going to grab this guy, bring it over and grab this guy, bring it over. The equal sign stays exactly where it is. Right? Negative three comes over the equal sign. It's sign changes. So this becomes three. Negative X moves over the equal sign, it's sign changes. So not that becomes X. So X is equal to three. Okay? Let's go, let's take a look at multiplication and division and see how we deal with those things. And you should be familiar with this if you aren't already, and if you're just getting into this stuff, keep in mind, if you do the equal sign means if you do something on one side of the equation, you have to do it to the other side of the equation, and if you want to move something from one side, or if you want to get rid of something on one side, you have to do the opposite to it. And if you're going to do it on one side, you have to do the opposite to the opposite. Let's go do division multiplication.