Solving One-Step Equations
Math
We're going to look at a few one-step equations.
In this video we're going to look at a few one step equations. In this first equation we have some number plus 6 equals 18. Now you may already know the answer to this right off the top of your head or you might be able to guess and figure out the answer. But I would encourage you to learn the process and to follow the steps so that when you get to an equation that you don't know the answer right away, you'll still know what to do. And as you move forward in algebra, you're going to get to some harder equations, so it's important to practice the steps on the easy ones so that you know what to do when it gets harder. So the main idea when you're solving an equation is that you're trying to get the variable all by itself. So we need to get this X by itself on the left hand side.
To do that, we need to move this plus 6. And to move things over, we use what are called inverse operations. Inverse operations are operations that undo each other. They cancel each other out. So if you want to undo addition, you can use subtraction. Addition and subtraction are called inverses. They can cancel each other out. So if we want to undo adding 6, we need to do the inverse operation and we need to subtract 6. And you want to think of an equation as a balance scale, and so that balance point is right in the middle where the equal sign is. So if you do something on the left hand side, they're not going to be balanced anymore in one side will weigh more than the other. So to keep things balanced, you always have to do the same thing on both sides.
So if we subtracted 6 on the left hand side of the equal sign, we want to subtract 6 on the right hand side too. So this plus 6 will cancel out the -6 and all that's left is an X and then 18 -6 is 12. Some teachers will actually have you draw a line down from the equal sign and that can help you separate the left side from the right side. So we said the answer was 12, and this is pretty easy to check. If we plug in 12 for X, we get 12 plus 6 equals 18. Does 12 plus 6 come out to 18? Yes. So we know our answer is right. Let's look at the next one. In this equation, we have some number minus three comes out to four. Now once again, this is pretty easy to guess the answer, but let's practice the steps and let's practice using the inverse operation. In order to get X by itself, we need to get rid of this minus three. To undo subtracting three, we need to use the inverse of subtraction, so to cancel out subtraction we need to use addition.
So we can cancel out a minus three by adding three to both sides. This minus three and plus three cancel out, so it's just an X left over. And then four plus three is 7. This is pretty easy to check too. We just plug in 7 for X 7 minus three equal four. Yes, so we know we have the right answer. And this next one we have a four right next to an X anytime you see a number right next to a variable. That means they're being multiplied. So in this problem, we have four times some number has to come out to 32. You probably already know the answer, but let's practice using the steps. To undo multiplying, we need to use the inverse of multiplication. The inverse is division, division can cancel out multiplying. So to undo multiplying by four, we need to divide both sides by four. So multiply them by four and divide them by four of those cancel out, so it's just an X left over. And then 32 divided by four is 8. We can check our answer here, too, if I just plug in an 8 for X four times 8, does that equal 32? Yes.
So these are always easy to check your answer. Make sure you plug it back in. If I plugged it back in and it came out to a different number, I would know to go back and try to fix my mistake. In this last one, I have X being divided by 5, so the undue division I need to use the inverse and multiply to the undue dividing by 5, I need to multiply both sides by 5. So multiplying by 5 and dividing by 5 those cancel and I get X equals 20, I can check it by plugging the 20 back into the original problem. This 20 divided by 5 equals four, yes. So I know this answer is correct too.