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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 be able to solve the two types of subtraction equations that you will come across. Learn the steps required to solve each type.

Sam has math class first thing in the morning. He likes to get it over with as soon as possible. Today though, Sam's teacher just happens to be in such a great mood that she gives everyone a pop quiz. This quiz is about solving **subtraction equations**, which are equations that involve the subtraction operation. In these types of problems, instead of seeing a complete equation like 12 - 10 = 2, Sam sees a problem like *x* - 10 = 2. It is Sam's job to figure out what the missing number is, represented by the *x*. How can he do this?

To figure out what the missing number, or *x*, is, Sam remembers that he needs to find a way to get the *x* by itself.

Right now, the problem has a -10 connected with the *x*. In order to make that -10 disappear, Sam needs to add a 10. Sam also remembers the addition property of equality, which says that he needs to add the same thing to both sides in order for the equation to remain the same. See, if the equation doesn't remain the same after making a change, then the answer won't be the right one.

So, if Sam adds a 10 to the left side of the equation, he also needs to add a 10 to the right side of the equation. *x* - 10 + 10 = 2 + 10. Simplifying both sides gives Sam an answer of *x* = 12. So 12 is the missing number in this problem.

Now, what if Sam was looking at this problem: 12 - *x* = 2? What can he do now? The *x* is now a -*x*. Sam doesn't want the *x* to be negative, so Sam decides to add the *x* to both sides. This changes the *x* to a positive, and it makes the *x* move to the other side of the equation. 12 - *x* + *x* = 2 + *x* becomes 12 = 2 + *x*.

Sam now has an addition problem. Sam can rewrite the problem so that the *x* is on the left side again. 2 + *x* = 12. Sam remembers that to make the 2 disappear so that the *x* is by itself, he needs to subtract the 2. Sam also remembers the subtraction property of equality, which says that he needs to subtract the same thing from both sides of the equation so that the equation stays the same. So Sam goes ahead and subtracts 2 from both sides of the equation. 2 + *x* - 2 = 12 - 2. Sam gets *x* = 10 for his answer.

Sam can check his answers by plugging them back into the original problem. After plugging in his numbers, he gets 12 - 10 = 2. Sam asks himself, is this a true statement? Does 12 - 10 really equal 2? Yes it does. So that means that his answer is correct.

Sam continues with the pop quiz. Here's his next problem:

*x* - 45 = 3

Sam sees his *x* with a -45. So, he knows that he needs to add 45 to both sides of the equation to solve. *x* - 45 + 45 = 3 + 45. This gives Sam an answer of *x* = 48. Is this correct? Plugging it back into the problem, Sam gets 48 - 45 = 3. Is this true? Yes, it is. So 48 is the correct answer.

Sam now sees this problem:

34 - *x* = 11

Sam sees that here he has a -*x*. He needs to add *x* to both sides of the equation. 34 - *x* + *x* = 11 + *x*. He gets 34 = 11 + *x*. Rewriting, he gets 11 + *x* = 34. This is now an addition problem. Sam now subtracts 11 from both sides of the equation. 11 + *x* - 11 = 34 - 11. Sam gets an answer of *x* = 23. Is this correct? Sam checks. 34 - 23 = 11. Does this work? Yes, it does. The correct answer is 23. Sam has finished the pop quiz, and he's very confident that he answered all the problems correctly!

What have we learned? **Subtraction equations** are equations that involve the subtraction operation.

To solve a subtraction equation where you have a missing value minus another integer and equaling yet another integer, you need to add the integer that is being subtracted to both sides of the equation. To solve a subtraction equation where you have an integer minus a missing value and equaling another integer, you first need to add the *x* to both sides of the equation. You can rewrite the problem so that the side with the *x* is on the left. Then you need to subtract the integer that is now being added to the *x* from both sides of the equation to solve. To check your answers, you can plug them back into the problem to see if it is correct.

Once you've completed this lesson, you should be able to:

- Define subtraction equations
- Explain how to solve a subtraction equation with two-digit integers

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10 in chapter 11 of the course:

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

- Finding the Absolute Value of a Real Number 3:11
- Absolute Value & Opposite Integers 4:23
- Integer Inequalities with Absolute Values 7:51
- How to Compare Integers 4:03
- Adding Positive & Negative Integers 6:30
- Addition Equations with One-Digit Integers 4:17
- Addition Equations with Two-Digit Integers 3:55
- Adding Three or More Integers 7:14
- Subtraction Equations with One-Digit Integers 6:21
- Subtraction Equations with Two-Digit Integers 5:35
- Dividing Integers: Rules & Terminology 6:03
- Multiplying Integers: Rules & Examples 10:53
- Go to 6th-8th Grade Math: Integers

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