Video: Creating Linear Equations with One Variable

Twelve more than half of a number is four less than the product of two and the number. Write an equation to represent the statement above. Let 𝑦 represent the number.

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Video Transcript

12 more than half of a number is four less than the product of two and the number. Write an equation to represent the statement above.

Let 𝑦 represent the number. As the number is represented by 𝑦, half of the number can be written as 𝑦 divided by two. 12 more than half of the number means that we can add 12. This gives us 𝑦 divided by two plus 12. We’re told this is equal to four less than the product of two and the number.

The product of two and the number can be written two 𝑦, as the product means multiply. Two multiplied by 𝑦 is equal to two 𝑦. As our answer is four less than this, we can subtract four, two 𝑦 minus four. This leaves us with the equation 𝑦 divided by two plus 12 is equal to two 𝑦 minus four. This represents the statement 12 more than half of a number is four less than the product of two and the number.

In this question, we were only asked to write the equation. However, we could use this equation to work out the value of 𝑦, the number. Multiplying both sides of the equation by two gives us 𝑦 plus 24 is equal to four 𝑦 minus eight. Adding eight to both sides of this equation gives us 𝑦 plus 32 is equal to four 𝑦. Subtracting 𝑦 from both sides of this equation gives us 32 is equal to three 𝑦, or three 𝑦 is equal to 32. And finally, dividing both sides of this equation by three gives us a value of 𝑦 of 32 divided by three, or thirty-two thirds. Therefore, the number that satisfies the equation 𝑦 divided by two plus 12 equals two 𝑦 minus four is 10 and two-thirds.

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