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Which algebraic expression represents this word description?

The product of seven and the difference between a number and ten.

A. [tex]7(10-x)[/tex]
B. [tex]10-7x[/tex]
C. [tex]7(x-10)[/tex]
D. [tex]7x-10[/tex]

Sagot :

GinnyAnsweridn
To solve this problem, let's carefully interpret the word description given: "The product of seven and the difference between a number and ten."

1. Identify the difference between a number and ten:
- Let the unknown number be represented by [tex]\( x \)[/tex].
- The difference between this unknown number and ten can be expressed as [tex]\( x - 10 \)[/tex].

2. Find the product of seven and the previously identified difference:
- We're asked to multiply seven by the difference [tex]\( x - 10 \)[/tex].
- The product of seven and [tex]\( x - 10 \)[/tex] is written as [tex]\( 7(x - 10) \)[/tex].

Now, we match our result with the given options:
- Option A: [tex]\( 7(10 - x) \)[/tex] - This is not correct as it reverses the difference.
- Option B: [tex]\( 10 - 7x \)[/tex] - This changes both the operations and their precedence, which is incorrect.
- Option C: [tex]\( 7(x - 10) \)[/tex] - This matches our result perfectly.
- Option D: [tex]\( 7x - 10 \)[/tex] - This represents the product of 7 and [tex]\( x \)[/tex] with 10 subtracted afterwards, which does not follow the word description accurately.

Therefore, the correct algebraic expression is:
C. [tex]\( 7(x - 10) \)[/tex]
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