How to Multiply and Divide to Solve Equations

In this lesson let’s learn how to multiply and divide—multiply and divide to solve equations. We are given two problems, the first one says solve (-5B = 25) and we should check our answer. Let’s do that one first. What is the equation given to us? (-5B = 25). As I can see B is called the variable, right? And if I have a variable I am multiplying by a number, right? Multiplication and division are inverse operations, okay? You know they are inverse operations then what I can do is if I’ve got a variable B being multiplied by a -5, I can divide it by a -5 to undo the multiplication, so let’s try this. Let’s write (-5xB=25) what we will do is divide it by a -5 on the left and divide it by -5 on the write. Any operation that I do, this is a division sign, has to be done to the left side of the equation and the write side of the equation. That’s the only way we can do this. So since we divided the left and the right by -5, we’re okay. So (-5B/ -5 = 25/ -5) okay? Let’s create a little nit more space. What do I get? (-5/-5 is 1) so B is the only thing that’s left equals (25/-5) which is -5 so the answer seems to be (B = -5). In order for us to check the answer, let’s replace the value of B as -5 here. So let’s take (-5x-5=25). All I did was I took the letter B the variable B and instead of B, I wrote down -5 which is the solution that we came up with. So if that is true, (-5x-5) should be equaled to 25. Is this correct? Well 5x5 is 25 and negative and negative when multiplied give us a positive so (+25 = +25) on the right. This is indeed correct which means (B = -5) is the answer.
Let’s try the second one, solve (–B/3 or –B ÷3 = 7) okay? (-B÷3=7). I am going to take some extra space. Since the variable –B or the variable B is being divided by a 3, this is a division equation, right? This is a division equation and if it is a division equation I can use a multiplication to undo it, okay? So let’s undo it by multiplying by the value of 3. So –B/3 let’s multiply by 3 on the left side of the equation and on the right side let’s multiply by 3 as well. So 3 and 3 will get cancels but the left side will be left with –B because 3÷3 is 1 right? So (–B=7x3) which is 21. So if the negative value of B is 21, (B= -21), okay? All I can do is move the negative sign from left to right. So if B=21 is indeed the answer, then I should be able to check it. -B/3=7, instead of B I am going to write 21, right? Actually it’s -21 right? The answer we came with was -21. So the negative signs stays outside then instead of B, I put down negative 21/3 should be equal to 7. Negative times negative is positive right? So 21/ 3—21/3 what is it? Is it 7? 21÷3 is indeed 7 and this is correct. If this is correct that means the solution we came up with (B= -21) is indeed correct, okay? So the solution to this equation solving for B, the answer is -21.