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How to Solve Simple Equations Involving Addition and Subtraction

Here’s that equation again: x + 6 = 10. We want to know how to solve this. What is the numerical value of x?

I’m sure you can work it out in your head because this is a very easy example. I’m sure you know that the answer is x = 4. Well, good thinking, but let’s work out the method for solving the equation using this easy example so that later, you know how to work out much harder equations that you can’t do in your head.

Okay then. I’ve already told you that we have to keep both sides of the equation equal to each other. What we need to do is work out how to get the x alone on one side, because once we’ve done that, whatever’s on the other side is the answer.

So, how do we do that?

x + 6 is on the left side. What we need to do is get rid of the + 6. What should we do? Did you say we need to subtract 6 from that side? That’s great if you did. We need to do the opposite operation. It’s a + 6, so we need a – 6. Addition and subtraction are opposite operations, aren’t they?

To keep the balance, we need to do the same thing on the other side of the equal sign, so on the left, we have x + 6 – 6, and on the right, we have 10 – 6. I have to say this again because it’s terribly important. You have to do exactly the same thing to both sides of the equation. Don’t forget that.

Now, on the left, we have + 6 – 6, and that would be x all by itself, which means that whatever we get on the right is the value of x. 10 – 6 = 4.

x = 4. See, it works.

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