 In this video, I'm going to talk about solving linear equations using distributive property. Again, linear equations are just lying type of equations. They have only one variable, usually only one variable, using distributive property. Distributive property is something that we learned in a previous video. So when solving any type of equation, the idea is to get the variable by itself. So in this case, I have two equations, but notice that both equations are the same. Actually, I'm going to show you two different ways to do this. One is using the distributive property and one is not using the distributive property. Okay, so again, the idea is to get the variable by itself. In this case, I want to get p, I want to get this variable by itself. So I've got to get rid of everything here on this left side. I've got to get rid of this negative 3, I've got to get rid of this 2, and I've got to get rid of this 3. So all that, I've got to get rid of. So the first way of solving this I'm going to show you is with distributive property. So what I'm going to do is I'm going to take 3 and I'm going to distribute it to both of the terms inside. 3 times 2 is 6. 3 times negative 3p is a negative 9p. And then this 42 equals 42, that just kind of drops down. When we distribute the 3, it's only inside the parentheses. We don't distribute it to the 42. Okay, now our numbers have changed a little bit with the idea, the concept of what we're trying to do is still the same. I still want to get rid of this negative 9. I still want to get rid of this 6 to get the variable by itself. All right, so now in this case, what I want to do is, now when you solve equations, one way I have seen somebody explain this is you want to do the kind of the opposite of your order of operations. When you look here, I see a plus 6 and I see a times by negative 9. Times by negative 9. So you kind of want to do the opposite of that. You want to do your adding and subtracting first and then you will do your multiplying and dividing. So basically that tells me I want to get rid of this 6 first and then I want to get rid of the negative 9. So to get rid of this 6, it's a positive 6. So to get rid of it, I want to subtract 6 from both sides. Now remember, whenever you do anything in an equation, add or subtract, multiply, divide, you've got to do it to both sides. So in this case, we're subtracting 6 from both sides. 6 minus 6 is 0. And in this negative 9, P is not affected. And then 42 minus 6 is 36. And again, still try to get the variable by itself. The only thing I have left is that negative 9. The negative 9 is multiplying times the variable. So what I want to do is I want to do the opposite. I want to divide by negative 9. The opposite of multiply is divide. So the negative 9's are going to cancel. All I'm left with is P. And 36 divided by negative 9 is going to be a negative 4. So in this case, the variable is equal to 4. Now you can check this if you would like to. This is what's great about solving equations is you can always take your answer that you get and plug it back into your original equation. So take this number. And if you plug it back in, you should get 42. You can actually do that rather quickly. Negative 3 times negative 4 is a positive 12. Positive 12 plus 2 is 14. 14 times 3. Yeah, 14 times 3 is 42. So now it doesn't work. All right, now I showed you solving that equation using the distributive property. Now I'm going to show you again without using distributive property. This is just a different way of solving the equation. OK, so looking at this left, or excuse me, looking at the right side, I have to get rid of, I want to get this variable by itself. So I've got to get rid of negative 3. I've got to get rid of this 2. And I've got to get rid of this 3 on the outside. But instead of taking that 3 and distributing it to the entire parentheses, what I'm going to do is I'm actually going to get rid of this 3 first. This 3 technically is multiplying times the variable. This 3 out here is multiplying times the variable. So to get rid of it, I want to divide by 3. 3 here is multiplying times the variable. So to get rid of it, I want to divide by 3, which means I've got to divide by 3 on this right side also. 3's are going to cancel. This 3 is not going to affect what's inside the parentheses. It cancels right here. But again, it's the idea. We want things to go away. We want the cancel, or 0, whatever it is. OK, so that cancels. I'm left with 2 minus 3p equals 3 goes to 4 once. 3 goes to 12 four times, or 14. I don't need parentheses anymore over here because I don't have any numbers out front. So parentheses are worthless. All right, so kind of the same deal here. I want to get rid of the 2 first, and then I'll get rid of the negative 3. So I want to subtract 2. Subtract 2 from both sides. Negative 3p is equal to 12. And then I want to divide by negative 3. And so p is equal to negative 4. So notice the answer is that we got both variables. Either way of solving it, you're going to get negative 4. That happens in mathematics a lot. There's going to be multiple ways of coming to an answer. You just got to figure out what you like best. So do you like using distributive property? Or do you want to get rid of the numbers first and then start solving? Both variations will work. It just kind of depends on what you like to do better and what you're more comfortable with. OK, and then I will do more examples in another video. But that is solving linear equations using the distributive property.