 Because we have no note sheet for this section, you're going to do all of your work in your notes. Get your notebook or your notes book out and be prepared to construct a flow proof. When designing a proof, remember one of the five essential steps to a good proof was writing down the given. And another one of those essential steps was writing down the proof. So for this proof, you're going to write down the given and the proof. The given is the hypothesis part of the conditional if-then statement, and the proof is the conclusion of the if-then statement. So now we have set up the given and proof for our proof. Now we can start to construct the proof itself. The first step will be to write down the given statement. We start with the given. We box in our statements in a rectangle, and we always have a reason for every statement. In this case, the reason for the statement is it was given. The first step to solving this equation would be to get the two variables on the same side of the equation. So I'm going to subtract A from both sides. If it helps you to make that note that you're subtracting A from both sides, go right ahead. When I subtract A from both sides, I get that 15 equals 6A minus 2. The reason I can make that statement is because I subtracted the same thing from both sides. So I'll call that the subtraction property of equality. And I have my next step. My next step to solving would be to add two to both sides of the equation. When I do that, I will get, oops, this is supposed to be 21. So instead of adding two, I will add 21 to both sides of the equation. So my new statement will be 36 equals 6A. And in this case, I added something to both sides, so I will call that the addition property of equality. My next step in solving this is to divide both sides by 6. And I will get that 6 equals A. My reason for that is the division property of equality. And now I have proven what I wanted to prove. So I will say QED. There you have a good, well-laid-out proof with your given, your prove, a constructed deductive reasoning set of steps, and the conclusion matching your proof statement. Make sure you have this complete work in your notes, because you'll need it as a reference when we get to class and have to construct the algebraic proofs for homework.