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Subtraction Equations with Two-Digit Integers

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  • 0:01 Subtraction Equations
  • 0:39 Solving Them
  • 3:09 Example 1
  • 3:46 Example 2
  • 4:44 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 be able to solve the two types of subtraction equations that you will come across. Learn the steps required to solve each type.

Subtraction Equations

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?

Solving Them

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.

EXAMPLE 1

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

x - 45 = 3

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