How to Solve Algebra Equations Using Inverse Operations

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One way to solve many different types of Algebra equations is through the use of inverse operations. Learn how to solve Algebra equations using inverse operations with help from a physics professional in this free video clip.

Part of the Video Series: Measurements & Other Math Calculations
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Hi. My name is Julia. Today, I'm going to show you how to solve algebra equations using inverse operations. So we're just today going to do simple one-step algebra problems. Let's start with a problem like X plus 5 equals 9. Now, I'm sure that just looking at this, you can figure out that X probably equals 4, but we want to use algebra to solve for X, so that when the problems get more complicated, you're not just doing it all in your head, you know the proper steps to take to solve more complex equations. In this case, we're going to use the inverse operation. So we look at what is going on between X and 5, because we want X alone, and what we have is addition. So in order to get X alone and get rid of the 5, we're going to do the inverse of addition, which is subtraction, and we're going to subtract 5 from both sides. Whatever you do to one side, though shalt do to the other side, in order to preserve the equality of each side. So when we subtract 5 from this side, these cancel out and we just get X, and 9 minus 5 is 4. If you had another problem, like X minus 3, equals 7, we look at the operation between X and the number that we want to move over to the other side, which is 3 in this case, and we see that we are subtracting. The inverse of subtracting is addition. We will add 3, again, to both sides. -3 plus 3 cancels out, we get X on this side, and 7 plus 3 is 10. X equals 10. I'm going to give you two more quick ones. If I have X divided by 2 equals 5, X is being divided by 2. The inverse of division is multiplication, so I'm going to multiply both sides by 2. Multiply by 2, multiply by 2. 2 over 2 crosses out, and I have X equals 5 times 2 is 10. And then the last one, if I have 2 times X equals 8, the inverse operation of multiplication is division, so I'm going to divide by 2 from both sides, remember that. 2 over 2 cancels out, I get X equals 8 divided by 2, is 4. So that's how you solve simple algebraic problems using inverse operations, which will make the more complicated algebraic problems a lot easier once you get the hang of this style. My name's Julia. Thank you.

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