# Writing & Solving Addition Equations with One Variable

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• 0:01 Writing an Addition Equation
• 2:11 Solving an Addition Equation
• 3:37 Example 1
• 4:13 Example 2
• 4:49 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how to properly write an addition equation and how to solve any addition equation that you come across. Learn what the steps are to solve these equations that have one variable in them.

## Writing an Addition Equation

In this video lesson, we talk about writing and solving addition equations with one variable. An addition equation with one variable is an addition equation that has one unknown number that you need to solve for. Your equation has an equals sign telling you what is equal to what. With this information, you will be able to find what your unknown number is. Why do you need to know this kind of information? Well, you will come across these kinds of problems in your math tests and such.

You will also come across these problems when solving real-world problems, such as when you need to figure out how much more of something you need. For example, say you have a five gallon jug. You already have three gallons in it. You will need to write an addition equation to solve this problem to figure out how many more gallons you need to fill it up. In this video lesson, we talk about the proper way to write these addition problems. Writing an addition equation from a word problem is considered in another lesson.

Let's see what the proper way is to write our addition problem for filling our five gallon jug. A proper addition equation has an equals sign. One side gives you the total. The other side tells you what things are being added together. Any one of your numbers can be a variable. Your variable will usually be written as x, but it could be written using any of the letters in the alphabet. For our problem, we will have 5 on one side because that is the total number of gallons we have. The other side will have 3 + x because we already have three gallons in the jug and we need to add an unknown amount to the jug to fill it up. Our complete addition equation is 3 + x = 5. This is something we can solve using algebra skills.

## Solving an Addition Equation

To solve our equation, we need to use an inverse operation because our variable has something attached to it. In this case, our variable has a 3 being added to it. In order to get the x by itself, we need to separate the plus 3 from the variable. To do this, we use the inverse operation, which is the opposite operation. In this case, this operation is subtraction. We need to subtract 3 from both sides of the equation. We need to do the same operation on both sides of the equation so that we don't change our equation and so that we will get the right answer. Subtracting 3 from both sides, we get 3 + x - 3 = 5 - 3 which turns into x = 2. This tells us that we need to add 2 gallons to our five gallon jug to fill it up. So, 2 is our answer.

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