 This video will talk about the addition property equations. So a linear equation can be written as AX plus B equals C, and when you look at that you're thinking, wow, there's a lot of variables in that. Well, there's really only one variable. The X is the variable here, and A, B, and C are going to be numbers. Okay, so it won't have a whole bunch of variables, just one variable, everything else is filled in with numbers. And A can't be zero, otherwise we just have B equals C. Okay, so when we look at an equation we need to remember that both sides are supposed to be equivalent. They may look different, but they are the same thing on both sides. So if it's equivalent, think of like a balance. Okay, when you think about a balance, when things are balanced you have the same thing on both sides, right? But if it's unbalanced, then you have something more on one side than the other side. Well that's not equivalent, so we need to keep this balance idea going. Think about the scales, and whatever you do, if I had this scale over here where I had two things and I wanted to keep them balanced, then I would have to take this one and take it off, but to keep it balanced I'd have to take that one, the same weight off of the other side. So that's what we have to do with equations. We have to take the same thing from both sides. So the goal that we're trying to get to is x equals something or something equal x, where x is on one side all by itself, 1x. And if we keep things organized, it shouldn't be too difficult. So here's the process that we're going to do. A equals C is going to be the kind of idea that we have. Something on the left hand side equal to something on the right hand side. If I add the same thing to both sides, then it's still equivalent. And if I subtract the same thing from both sides, it's still equivalent. So let's look at this example. We have x plus 2 equal 5. I want to get to x all by itself, but I'm adding 2 to it. How would I take the 2 off of that side? Well, to take it off of that side, I would have to subtract it away. But if I subtract it from that side, I have to subtract it from the other side as well. And now over here I have x, because this cancels itself out, equal to 5 minus 2, which is 3. And now I have x equal 3 x by itself. I can always check to make sure that I did it right by just plugging and chugging. So instead of x, I'm going to have 3 plus 2 equal 5. Well, 3 plus 2 is 5, and that is equal to 5. So we know that we found the right answer. Let's try this problem. I have x minus 4 equal to negative 8. I want to again get x by itself, but I'm subtracting 4 from it. So in order to take and get rid of that 4, I have to do the opposite. I have to add 4. And if I do it to one side, I have to do it to the other side. Remember, we're keeping that balance idea going on. So these two things cancel each other out, so I just have x on this side. And then negative 8 plus 4 will be negative 4. All right, let's check it. So it says that x, which we now found to be negative 4, minus 4 is supposed to be equal to negative 8 if we did it right. And negative 4 plus a negative 4, if you need to do it that way, gives us negative 8 on this side equal to negative 8. So we know that we found the right answer. Let's look at these examples then. So x plus 10 equal negative 12, we want to subtract 10 from both sides. Notice I'm keeping everything organized. I'm adding underneath the same kind of terms. I'm bringing down what's left over. I'm bringing down my equal sign. And then I'm going to add over this side or subtract whatever the problem is. Negative 12 plus a negative 10 will be a negative 22. And if you weren't sure about adding or subtracting, find out what you have and then check to see if you did it right. So we have x, what you're saying is negative 22 plus 10. And that should be equal to negative 12 if we did it correctly. Negative 22 plus 10, the difference is 12. And negative 22 is larger, so it's a negative 12 equal to a negative 12. So we know that x is equal to negative 22. Now, this time we have a fraction, it doesn't make it any different. This is just a number, it's a real number, and I want to get x by itself. So I'm just going to add four ninths to both sides. Now, if you don't like it being up and down, you could say negative 2 over 9 plus 4 over 9. I think a lot of us like to see it across instead of up and down. It's the same thing. What I'm doing right there is this part right here. And when we get that, we see that we have a positive 2 over 9. The difference is 2 and 4 is larger. So these cancel out. On this side, I have x equal 2 over 9. So to check this, we're going to have x, which is now, we know to be 2 ninths, minus 4 ninths, and it should be equal to negative 2 over 9. And 2 minus 4 is a negative 2 over 9 equal to negative 2 over 9. So we know that x is equal to 2 ninths.