Have you ever done a math problem and then looked at your answer and you're like, I'm not sure if this answer is really correct. I think I did everything right and the answer makes sense, I guess. But there may not be a way to know for sure if your answer is right, unless maybe you have a teacher or someone else check your your steps for you. Well, the cool thing about solving equations is that you can always know whether your answer is correct or not. And that's what this lesson is going to focus on. How you can check your own answer so that you will know 100% for sure if your answer is correct. Or if it's not correct and you need to go back and maybe double check your steps. So here are the steps for checking your answer. The first step is to substitute your answer for the variable in the equation. Now, we did this a little bit when we learned about how to evaluate expressions for a value. It’s very similar to that. So if you want to go back and check that lesson out for a review, that would be helpful. Now, once you substitute your answer for the variable, you want to simplify both sides of the equation. So that means that whatever addition, multiplication, or any other operations need to be done, you just go ahead and do those to simplify both sides. And then if the resulting equation that you get after both sides are simplified, if it's a true equation, then that tells you that your answer is correct. Now, this is the first time that we've talked about an equation being true. So what does that mean? What is a true equation? Here are some examples. True equations are really just equations that make sense. For example, five equals five. Well, that is true. Five is five. So that's true equations: 12 equals 12, 39 equals 39. Simply put, if you have the same thing on both sides of the equation, then it's a true equation. So when we simplify our answer after we substitute it in and we see a true equation at the end, then that means that our answer was correct. On the other hand, if you see something that's a false equation, then that means our answer was not correct. So what is a false equation? These are equations that just don't make sense at all. Seven equals 15. Well, that's not true. Seven isn't equal to 15, so that's false. 21 equals 22. No, that's not right. Or 30 is equal to 300. No, that doesn't make sense at all. So when you have two different numbers on each side of the equation, then that tells you you have a false equation. And that means that our answer that we got for our variable was not correct. So let's look at some examples to see if these numbers really are the answer. So is seven a solution to y plus three equals ten? First we want to focus on our equation. And then let's just write it down separately so we can see it clearly. Y plus three equals ten. And now we want to see if seven is the solution is the answer for this equation. So we're going to substitute seven for our variable, which is y into our equation. And it will look like this seven plus three equals ten. Now our next step is to simplify both sides of the equation. So on that left side we have seven plus three. We can simplify that and it becomes ten. On the right side, we just have the number ten. It's already simplified, there's nothing else we can do to it. So we just bring it down and we look at our resulting equation. So now we have ten equals ten. Well, hey, that's true. Ten is equal to ten. So that means that seven is a solution to the equation. Y plus three equals ten. Let's look at another example. Is 4 a solution to 2m minus five equals six? Here's our equation. So write that down. Two M minus five equals six. And we want to see if four is a solution. So we want to see that if we plug four in for M, if it will give us a true equation or not. Now notice where m is positioned in our equation. We have that two that's written next to it. And remember, that means that two is being multiplied by M. So when we plug that four in for M, we need to make sure that we show that we are multiplying the two times the four. So we can write it like this. We can use parentheses to show the multiplication. Two times four minus five equals six. Now let's simplify both sides of the equation. Now on that left side we have two times four minus five. We have a couple of things going on there, so that means that we need to make sure we follow the order of operations to simplify it. The multiplication will always get done before the subtraction. So the two times four becomes eight. Let's bring everything else down for now. Now we can do the subtraction. Eight minus five will give us three. On the other side we have just the six. It's already simplified, so let's just bring it down. Now our resulting equation is three equals six. Wait a minute, that doesn't make sense. Three is not equal to six. This is a false equation. So that means that four is not a solution solution to our equation. Two m minus five equals six. So when you come across something like this, that would tell you to go back and check your steps for solving the equation. You may come up with a different answer once you double check your steps.