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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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.

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.

If our variable was by itself already on one side of our equation, then all we need to do is to evaluate the other side of the equation. For example, if we have *x* = 3 + 5, all we have to do is to add the 3 and the 5. We get *x* = 8 for our answer.

Let's look at a couple more examples.

Write an addition problem that shows *x* + 4 on one side and 10 on the other side and then solve it.

This problem tells us what is on either side of our equals sign. We write *x* + 4 = 10. To solve this equation, we need to perform the inverse operation. We need to subtract 4 from both sides. We have *x* + 4 - 4 = 10 - 4. This turns into *x* = 6. Our answer is 6, and we are done.

Write an addition problem that shows 11 + *x* on one side and 10 on the other side and then solve it.

Our addition equation is 11 + *x* = 10. To solve this equation, we need to subtract the 11 from both sides of the equation. We get 11 + *x* - 11 = 10 - 11. This gives us *x* = -1 for our answer. Yes, some of our problems will give a negative number for an answer, and that is perfectly okay.

What have we learned now? An **addition equation with one variable** is an addition equation that has one unknown number that you need to solve for. To write a proper addition equation, you have an equals sign. One side shows you the total. The other side shows you what things are being added together. You can have a variable on either side of the equation. To solve an addition equation where the variable is on the addition side, you perform the inverse operation. The inverse operation, in this case, is subtraction. You subtract whatever is being added to the variable from both sides of the equation. If the variable is on the total side, then all you need is to evaluate the addition side.

You should be able to solve addition equations with one variable after completing this lesson.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Inverse Operations in Math: Definition & Examples 4:50
- Writing & Solving Addition Equations with One Variable 5:48
- Writing & Solving Subtraction Equations with One Variable 4:06
- Writing & Solving Subtraction Word Problems with One Variable 5:47
- Writing & Solving Multiplication Equations with One Variable 5:08
- Writing & Solving Multiplication Word Problems with One Variable 4:48
- Writing & Solving Division Equations with One Variable 5:06
- Writing & Solving Division Word Problems with One Variable 4:44
- How to Use Algebra Tiles to Model & Solve Equations 6:12
- Go to 6th-8th Grade Algebra: Writing & Solving One-Step Equations

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