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One-step addition equation

In this math lesson, we learn to solve simple equations with one variable. We isolate the variable by removing other terms on the same side. For example, if a + 5 = 54, we subtract 5 from both sides to find a = 49. Finally, we check our solution by substituting the value back into the original equation. Created by Sal Khan.

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Video transcript

Solve for a and check your solution. And we have a plus 5 is equal to 54. Now, all this is saying is that we have some numbers, some variable a. And if I add 5 to it, I will get 54. And you might be able to do this in your head. But we're going to do it a little bit more systematically. Because that'll be helpful for you when we do more complicated problems. So in general, whenever you have an equation like this, we want to have the variable. We want this a all by itself on one side of the equation. We want to isolate it. It's already on the left-hand side, so let's try to get rid of everything else on the left-hand side. Well, the only other thing on the left-hand side is this positive 5. Well, the best way to get rid of a plus 5, or a positive 5, is to subtract 5. So let's subtract 5. But remember, this says a plus 5 is equal to 54. If we want the equality to still hold, anything we do to the left-hand side of this equation, we have to do to the right side of the equation. So we also have to subtract 54 from the right. So we have a plus 5 minus 5. Well, that's just going to be a plus 0. Because if you add 5 and you subtract 5, they cancel out. So a plus 0 is just a. And then 54 minus 5, that is 49. And we're done. We have solved for a. A is equal to 49. And now we can check it. And we can check it by just substituting 49 back for a in our original equation. So instead of writing a plus 5 is equal to 54, let's see if 49 plus 5 is equal to 54. So we're just substituting it back in. 49, 49 plus-- let me do that in that same shade of green. 49 plus 5 is equal to 54. We're trying to check this. 49 plus 5 is 54. And that, indeed, is equal to 54. So it all checks out.