Video: Creating Linear Equations with One Variable

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œForty less than three times an unknown number is twenty.”

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Video Transcript

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œ40 less than three times an unknown number is 20.”

We’re told in the first sentence that the unknown number is equal to 𝑛. Three times this unknown number is equal to 𝑛 multiplied by three. We write this expression as three 𝑛. Our expression needs to be 40 less than this. This means that we need to subtract 40 from three 𝑛 giving us three 𝑛 minus 40. We’re also told that this expression is 20. This means that the full equation is three 𝑛 minus 40 is equal to 20. The equation that represents the statement 40 less than three times an unknown number is 20 is three 𝑛 minus 40 equals 20.

Whilst we’re not asked to in this case, we could solve the equation using two steps. Firstly, we can add 40 to both sides of the equation. Negative 40 plus 40 is equal to zero. So, the left-hand side simplifies to three 𝑛. 20 plus 40 is equal to 60. Therefore, three 𝑛 is equal to 60. We can then divide both sides of this new equation by three. Three 𝑛 divided by three is equal to 𝑛. And, 60 divided by three is equal to 20. The value of 𝑛 that satisfies the equation three 𝑛 minus 40 is equal to 20 is 20. Three multiplied by 20 is equal to 60. And, subtracting 40 from this gives us the answer of 20.

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