 So sometimes in classes you're asked to not just work with one variable you may have multiple variables and this is an example that you may see. So this is an equation that you probably seen before for temperature working with Fahrenheit and Celsius. In this particular one has been solved for Fahrenheit. Notice that what we're asked to do is to solve for Celsius. So our goal of course is to get the C completely by itself. Okay so first question. Is there anything I can simplify on the left? No. Is there anything I can simplify on the right? No. So we're ready now to move things and to do our solving piece. So notice that the letter that we're trying to solve for which is C is on the right hand side and notice that there are two things in the way of us having C completely by itself. We have 9 fifths and we have plus 32. You will always get rid of the addition or the subtraction piece before you ever touch anything that's being multiplied or divided. So notice that 9 fifths is being multiplied by C. I'm not going to touch the 9 fifths right now. I'm going to focus on the addition or subtraction piece which is the plus 32. So how would you move or get rid of a plus 32? The opposite of course would be to subtract 32 from both sides. Remember whatever you do to the left you have to do to the right. Now be extremely careful on this left hand side. F and negative 32 are not like terms so you can't combine them together. So you just basically write them side by side. So F minus 32. Bring down your equal sign and then on the right hand side you're still left with 9 fifths C and 32 minus 32 cancel out. The whole purpose was to remove that addition or subtraction piece first. Now still trying to solve for C which is here. Notice that the only thing bothering or in the way of us solving for C is the 9 fifths which is being multiplied by C. One option we could divide both sides by 9 fifths. That would get a little messy. There's an easier way a little trick to do this. That's a little easier to get that C by itself. So instead of dividing both sides by 9 fifths what we can do is we can multiply both sides by what's called the reciprocal. The reciprocal of 9 fifths is just the flip of it which is 5 over 9. Remember as long as I do it to both sides it's okay. And I want to start with the right hand side first. Why that's so important to multiply by the reciprocal? Notice have a 5 in the top a 5 in the bottom they cancel. Notice have a 9 in the top a 9 in the bottom they cancel. And right off the bat you can see that you're simply left with C. So an option is to multiply by that reciprocal when you're dealing with a fraction. On the other side of course I still have 5 ninths and then in parentheses F minus 32. So if I rewrite I'm just going to change the sides flip it. So if I have C equals and it's going to be equal to 5 ninths then in parentheses F minus 32. Again a formula that you have probably seen before. The original formula was solved for F. This one has now been solved for C or Celsius. So just working with temperature. Another problem with temperature. In this particular one we're still working with the same formula we were just a minute ago. But we're wanting to convert 72 degrees Fahrenheit to Celsius. I'm going to show you two different ways to do this. The first method. So we'll call this method one. Is to use the formula that we have in front of us and simply substitute in the 72 in place of the F. So I have 72 is equal to 9 fifth C plus 32. Again my goal is to solve for Celsius. So if you remember what we did just a moment ago. We're going to do exactly the same thing. We need to get rid of the 9 fifths and the plus 32 and I'm going to always start with addition or subtraction first. So to get rid of the positive 32 we're simply going to subtract 32 from both sides. So 72 minus 32 is going to give me 40. Hang on to your equal sign. And then on the right hand side we have 9 fifth C and 32 and negative 32 of course cancel out. See if you remember the little trick from just a moment ago. So I'm trying to get rid of the 9 fifths in front of the C. I could divide both sides by 9 fifths. But an easier quicker way is to multiply both sides by the reciprocal which would be 5 ninths. So let's see what happens. On the right hand side we'll start with that first. The 5's cancel. The 9's cancel and your left would see which was what you wanted in the first place. On the left hand side notice that I could rewrite 40 as 40 over 1 and I can multiply straight across. So 5 times 40 would be 200 and in the denominator 9 times 1 would be 9. Now you could leave it like that or we could also put it in the calculator and do 200 divided by 9. So C is approximately 22.2 or 22.2 degrees Celsius is approximately the same thing as 72 degrees Fahrenheit. So that's the first method. The second method, method two, would be to go back to what we just found a few minutes ago. In the last slide we found that Celsius is equal to 5 ninths parentheses F minus 32. We solved the formula already for Celsius. Could I plug the same thing in here and get the same answer? Should be able to. So let's do that. So in place of F I'm going to substitute in the 72. So C equals 5 ninths times 72 minus 32 and as we do this I want you to notice the relationship between method one. Okay first thing based on order of operations that I would do is what's inside the parentheses first. 72 minus 32 which is 40 and notice we came up with 40 over here as well when we did 72 minus 32. And then we're back to the same spot we were in the previous problem. I can put this over one and multiply straight across. Same place we were right here 5 ninths times 40 over one which we know gave us 200 over 9 which we know is approximately 22.2 degrees Celsius. So this is solving equations.