In algebra, we have certain principles that we use to help us solve equations quickly and easily.

The addition principle is one of them. Watch this video lesson to learn how you can apply it to solve your equations.

## The Addition Principle

The **addition principle** tells you that if you add or subtract the same thing to both sides of an equation, then your equation will remain the same. You can picture the addition principle by thinking of two equal piles of stuffed animals, one on the left and one on the right with an equals sign in between. What if you added some more stuffed animals to the left side? How would you keep the two piles equal to each other?You would have to add the same amount of stuffed animals to the right side. I mentioned sides, but the principle applies no matter which side you start with.

The same goes if you took away some stuffed animals from the right side. To keep the two piles equal, you would have to take away the same amount of stuff from the left side.Why is this useful? Well, when you want to solve an equation for a particular variable, you want to isolate your variable, or get it by itself. See, sometimes, you will see your variable being added or subtracted by a number. To solve and get your variable by itself, you would need to change this number to 0 so that it is no longer adding or subtracting from our variable.

In order to do this, you sometimes have to add or subtract a value from the side with the variable.But if you only did it to one side of the equation, your answer would be wrong. So, the addition principle tells you that you have to add or subtract the same thing to the other side of the equation as well so that your equation remains the same and your answer is correct. For example, for the equation *x* + 1 = 3, if we subtracted the 1 from the left side only to get *x* by itself, I would get *x* = 3.But is that a correct answer? If I plug in 3 for *x* in my equation, I would get 3 + 1 equaling 4. Does 4 equal 3? No! So, I can’t add or subtract from just one side; I have to do it to both. Think of your piles.

## An Example

Let’s solve *x* + 1 = 3 correctly now. We see that the side with our variable also has a plus 1. How do we make this plus 1 disappear or otherwise become 0? What can I add or subtract to this plus 1 to make it 0? I need to subtract a 1. The addition principle tells me that if I subtract a 1 from one side, I also have to subtract it from the other side. Let me see what I get when I do this.*x* + 1 – 1 = 3 – 1*x* = 2Ah, I get an answer of 2.

Is this correct? Let me plug it back into my equation to see. 2 + 1 = 3 becomes 3 = 3. Does 3 equal 3? I think so. I am done.

I have applied the addition principle, and my answer is correct!

## Second Example

Let’s try another one.*x* – 4 = 9I look and I see that my variable is on the left side. Hmm, but it’s not by itself.

It is being subtracted by a 4. How do I change this minus 4 to a 0? I would have to add 4. I start to add 4 to the left side. But wait, what does the addition principle tell me? It tells me that if I only add 4 to one side, then my equation won’t be the same and my answer won’t be correct.

I also need to add 4 to the other side. Oh, I’m so glad I remembered!*x* – 4 + 4 = 9 + 4*x* = 13Is 13 the correct answer? Let’s check by plugging it back in.13 – 4 = 9 becomes 9 = 9. Yes, another correct answer!

## Third Example

See if you can work this problem with me.*x* – 8 = 8What do we do to solve this?*x* – 8 + 8 = 8 + 8That’s right; we need to add 8 to both sides.*x* = 16I get 16. Is that the correct answer?16 – 8 = 88 = 8Yes, it is!

## Lesson Summary

This was a nice little video lesson, wasn’t it? What did we learn? We learned that the **addition principle** tells you that if you add or subtract the same thing to both sides of an equation, then your equation will remain the same.

This helps us solve problems when we have our variable being added or subtracted by a number that we want to move to the other side of the equation or otherwise make 0 on the side of the variable.We learned that if we see the variable being added by a number, then we subtract that number from both sides of the equation to solve it. Also, if we see the variable being subtracted by a number, then we add that number to both sides of the equation to solve it.

## Learning Outcomes

This lesson can provide you with the knowledge you’ll need to:

- Interpret the addition principle
- Solve basic equations using the addition principle