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Question Video: Understanding Inverse Operations to Find the Starting Number Mathematics • 7th Grade

I think of a number. I multiply it by 3 and then subtract 5. The answer is 13. What number did I think of?

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Video Transcript

I think of a number. I multiply it by three and then subtract five. The answer is 13. What number did I think of?

One way to answer this question is to set up an equation. We can begin by letting the number being unknown, in this case, 𝑥. We are told that we multiply the number by three. This can be written as three 𝑥. We then subtract five, so our expression is three 𝑥 minus five. As the answer is 13, we can turn this expression into an equation by setting it equal to 13. We can now work out the number by solving this equation. We can do this using the balancing method and inverse operations.

The inverse or opposite of subtracting five is adding five. Adding five to both sides of the equation gives us three 𝑥 equals 18 as negative five plus five is zero and 13 plus five is 18. Our final step is to divide three from both sides of this new equation as division is the inverse of multiplication. Three 𝑥 divided by three is equal to 𝑥, and 18 divided by three is equal to six. This means that the number that was initially thought of was six. We can check this answer by multiplying six by three and then subtracting five. As this does indeed give us an answer of 13, we know that the answer is correct.

An alternative method that could’ve been used in this question is using function machines. Once again, we start with the unknown 𝑥. We multiply it by three, subtract five, and end up with the answer 13. We can reverse this by carrying out the inverse operations. The inverse or opposite of subtracting five is adding five. And the inverse of multiplying by three is dividing by three. 13 plus five is equal to 18. Dividing this by three gives us an answer of six. We have once again proved that the original number was six.

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