# Video: Writing Algebraic Expressions

Which of the following expressions could be written as 4 − 3𝑥? [A] 4 minus the quotient of 3 and 𝑥 [B] 4 reduced by the difference of 3 and 𝑥 [C] 4 less than the product of 3 and 𝑥 [D] 4 diminished by the product of 3 and 𝑥

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### Video Transcript

Which of the following expressions could be written as four minus three 𝑥? a) four minus the quotient of three and 𝑥, b) four reduced by the difference of three and 𝑥, c) four less than the product of three and 𝑥, or d) four diminished by the product of three and 𝑥.

Notice in our expression, we have a three next to the 𝑥. This represents three being multiplied by 𝑥, also known as the product of three and 𝑥. It would not be the difference of three and 𝑥 nor would it be the quotient of three and 𝑥. And that means we’ve eliminated a and b.

Now, we need to consider if this is four less than the product of three and 𝑥 or four diminished by the product of three and 𝑥. Four less than the product of three and 𝑥 would look like this: three 𝑥 minus four. Four diminished by the product of three and 𝑥 would be starting with four and taking the product of three and 𝑥 away.

Only the fourth option, four diminished by the product of three and 𝑥, represent our expression. We can write four diminished by the product of three and 𝑥 as four minus three 𝑥.