Watch this video lesson to learn how you can solve subtraction problems where you need to find a missing value.

Learn what steps you need to take to easily solve these types of equations.

## Subtraction Equations

Jenny is on this game show where she needs to solve a **subtraction equation** correctly to win a prize. A subtraction equation is an equation where you have the subtraction operation going on.

For example, 6 – 3 = 3 is a subtraction equation. But for the game show, instead of seeing a complete equation like that one, Jenny needs to solve an equation like this: *x* – 3 = 3. The *x* stands for a missing value.

Jenny needs to find what the *x* equals. Let’s see what Jenny does.

## Solving

To solve the equation, Jenny realizes that she needs to use the addition property of equality, where she adds the same thing to both sides of the equation to keep the equation the same. She sees that she needs to add so that she can get the *x* by itself.

See, when the *x* is by itself, she will see that it will equal a certain value. Then, she will know what the answer is. If she adds a 3 to the left side, she will be left with an *x* on that side. To solve the problem, she also needs to add a 3 to the right side.

*x* – 3 + 3 = 3 + 3. This turns into *x* = 6. Her answer is 6.

What does Jenny win? She wins an ice cream maker!Now, if we have a problem such as 6 – *x* = 3, where the *x* is being subtracted, we will need to approach it a bit differently. In order to solve this type of problem, we first need to add the *x* to both sides of the equation so that the *x* turns positive. This actually moves the *x* to the other side of the equation. 6 – *x* + *x* = 3 + *x* turns into 6 = 3 + *x*. At this point, we can rewrite the problem so that the side with the *x* is on the left side. 3 + *x* = 6. This is now an addition problem.

To solve addition problems, we subtract what is being added to the *x* from both sides of the equation. 3 + *x* – 3 = 6 – 3 turns into *x* = 3. By subtracting from both sides we are able to get the *x* by itself and find our answer. Let’s go back to the show now.

## Example 1

Since Jenny won, she gets to play again.

This time, the problem is *x* – 8 = 2. To solve this one, Jenny sees that she needs to add an 8 to get the *x* by itself. So, she adds an 8 to both sides of the equation. *x* – 8 + 8 = 2 + 8. What does she get? She gets *x* = 10. Her answer is 10. Is this correct? The game show host pauses and then says ‘Congratulations! You’ve won the latest video game console with ten games!’This finishes round one of the game.

Since Jenny has given all correct answers so far, she gets to continue on to round two. But now the questions are a bit harder.

## Example 2

The first problem in round 2 that Jenny is given is 9 – *x* = -1. This is a bit different from the previous problems. Now, the *x* is the one being subtracted. Jenny needs to tackle this kind of problem a bit differently.

She knows that if she sees subtraction, she will need to add. The *x* is being subtracted, so Jenny goes ahead and adds the *x* to both sides. To find *x*, we do want to make sure that our *x* is positive and not negative. Since the *x* is being subtracted, it is negative. Adding the *x* to both sides will turn the *x* into a positive but it will make the *x* change sides. 9 – *x* + *x* = -1 + *x* turns into 9 = -1 + *x*.Jenny now sees that the *x* has switched sides.

She is more comfortable with the x on the left side, so she rewrites the problem like this: -1 + *x* = 9. This is interesting; the problem now has turned into an addition equation. Also, even though we have a negative 1, we have kept the negative sign with the 1 this whole time. Jenny remembers that to solve these types of problems, she now needs to subtract what is being added to the *x* from both sides to solve it.

Oh but wait, the -1 is actually telling us that the 1 is being subtracted. So, instead of doing the subtraction from both sides, we now do addition to both sides. So, Jenny adds a 1 to both sides of the equation.

-1 + *x* + 1 = 9 + 1. This turns into *x* = 10. Jenny tells the game show host that the answer is 10. Did Jenny win? Yes, she did! This time she won an all-expenses paid trip to Hawaii for two weeks!

## Lesson Summary

Let’s review what we’ve learned. A **subtraction equation** is an equation where you have the subtraction operation going on. When you have a subtraction equation where you have a missing value minus an integer and equaling another integer, you need to solve it by adding the number that is being subtracted to both sides of the equation.

But if you have an integer minus a missing value, then you need to tackle the problem differently. For this type of problem, you first need to add the missing value, the *x*, to both sides of the equation. This turns the *x* to a positive and makes the *x* switch sides. Now you can rewrite the problem so that the *x* is on the left. This is now an addition problem. To solve this type of problem, you now subtract what is being added to the *x* from both sides of the equation.

However, if this addition problem involves a negative number, instead of subtracting from both sides, you will actually add to both sides.

## Learning Outcomes

After this lesson, you should be able to:

- Define subtraction equation
- Explain how to solve a subtraction equation for a missing variable