 This video will talk about the multiplication property of equations. Basically, it says if we multiply the same thing on both sides, then we're going to stay equivalent. Or if we divide the same thing on both sides, we will stay equivalent. And then just remembering that dividing is like multiplying by the reciprocal of both sides. So if I want to get rid of, or if I want to divide by b on both sides, it's the same thing as multiplying by 1 over b. So let's look at these examples. And remembering that what you do to one side, you have to do to the other side to keep it balanced. So we have 10x equal to 20. Well, if I want x by itself, it's 10 times x, so I need to do the opposite or divide by 10. But if I divide one side by 10, I have to divide the other side by 10. So now I'm going to have my 10s cancel each other out. We have x and 20 divided by 10 is going to be 2. And we could check it. 2 times our 10 is equal to 20, and 10 times 2 is 20, which is 20. What if we have an example that looks like this one? x divided by 3 is equal to negative 8. Well, if we're dividing by 3, we always want to do the opposite operation to that x. So we want to multiply by 3. So we multiply both sides by 3, and we get the 3 becomes like 1, 3 over 3, and we just have x on this side. And negative 8 times 3 would be negative 24. And again, we can check it by saying negative 24 divided by 3 is supposed to be equal to negative 8. And negative 24 divided by 3 is negative 8. We know that it's true, and we found the right answer. And then we have a third example where it looks like a fraction is being multiplied by x. And we want to divide that fraction off. And to divide fractions, we just multiply by the reciprocal. So the reciprocal of 1 fourth would be 4 over 1. And we have to do that to both sides. It's really the same thing as multiplying by 4. So the 4's are a factor of 1, and the 1 over 1 is a factor of 1, so we just have x over here. And 6 times 4 is 24. Let's try. 1 fourth times 24 is supposed to be equal to 6. And 1 fourth times 24 would be 24 over 4. Equal 6 and 4 into 24 is 6. So we know we did it correctly. Now let's solve some equations that have multi-steps in them. Remember that when we do multi-steps, we're still trying to get to x by itself. So it's kind of like an onion. We want to peel the layers away. And the outer layer in this particular problem would be this minus 3. We're subtracting 3, so we have to do the opposite. So add 3 to both sides. And so we have x over 7 on the left-hand side. Equal to 1 plus 3, which is 4. And now we're dividing by 7, so the opposite to peel this layer away would be to multiply by 7 on both sides. So there's my factor of 1, and I just have x equal to 28. And if we checked it, we'd have 28 over 7 minus 3 is supposed to equal 1. 28 divided by 7 is 4 minus 3, and 4 minus 3 is 1. So 1 is equal to 1. There's our answer, x equal 28. Alright, peeling this onion. We have this plus 2, and we need to take it to the other side so that we can get to this x by itself. So we take this first layer off by subtracting 2. And when we do that, those cancel each other out because they're opposites. So I have negative 3x. We're subtracting 2 from both sides, but that would be the same thing as adding a negative 2. So we'd have negative 9. And now we need to divide by 3 to do the opposite operation. And x is going to be equal to negative 9 divided by negative 3, which is a positive 3. And if we checked it, negative 3 times 3 plus 2 is equal to negative 7. And negative 3 times 3 would be negative 9 plus 2. And negative 9 plus 2 is negative 7, and that is definitely equal to negative 7. Alright, so what if we have a really involved problem like this one? Where we start? Well, we start by combining like terms. We got to make it as simple as possible, and then we can see what we have to move. So we have a 7x and a 5x that we need to combine. So we really have 12x plus 4 on this side equal to 14x plus 3. Now remember, it doesn't matter if I move the constants first or if I move the variables first, but what I like to make my x positive. So if I'm going to do that, I have a 12x and a 14x. 14x is larger and it's positive on this side, so I want to subtract the 12x from both sides. I'm not dividing yet because I'm just moving it across the equal sign. The whole thing. I'm taking the x with it. So I'm going to subtract 12x from both sides, and that'll leave me with 4 on the left-hand side, and 14x minus 12x leaves me with 2x plus 3. And now I need to get this 3 away from my x. Now that I only have one x term, I know I have to move this 3, so I'm going to subtract 3 from both sides. And that will give me 1 is equal to 2x, and it's 2 times x, so I'm going to divide both sides by 2, and that tells me that 1 half is equal to x. And I'll leave the checking up to you for that one. 4 times the quantity 2 plus 15 is equal to 20. You see parentheses. We need to clear them. We've got to simplify the sides, and that includes distributive. So we need to multiply the 4 times everything inside. So we have 4t plus 60 is equal to 20. And now I have a t term and a constant on this side and a constant on the other side, so I want to subtract my 60 to get to that t term all by itself, and subtract 60 on this side. And we're going to have 4t left over here, because these are opposites. And 20 minus 60 would be a negative 40, and then 4 times 2 means we have to divide by 4. So t on the left-hand side equal to negative 40 divided by 4 will be negative 10. And again, I'm going to leave the checking for you to do. All right. And then the final one here is going to be distributing a negative. So remember, when you distribute a negative, you always want to watch your signs. So a negative times a positive is going to be a negative 12p, and a negative 3 times a negative 1 will be plus 3 equal to negative 12. We've got a positive 3 on this side, so we want to subtract 3 from both sides to get to that p term by itself. So negative 12p on the left-hand side is equal to negative 15. And if we divide by negative 12 on both sides, then p is going to be equal to a positive, because it's a negative divided by a negative, 15 over 12, but we can reduce that. So it should be equal to, they're both divisible by 3, so it should be equal to 5 over 4.