apaulus4907
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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]$7(x-10)$[/tex]
B. [tex]$7x-10$[/tex]
C. [tex][tex]$7(10-x)$[/tex][/tex]
D. [tex]$10-7x$[/tex]

Sagot :

GinnyAnswer
To determine the correct algebraic expression for the given word description, let's break down the description step-by-step.

### Word Description:
"The product of seven and the difference between a number and ten."

1. Identify the variables and constants:
- Let the number be [tex]\( x \)[/tex].
- The constant mentioned is 10.

2. Understand the phrase "the difference between a number and ten":
- This means we are subtracting 10 from the number [tex]\( x \)[/tex], giving us the expression [tex]\( (x - 10) \)[/tex].

3. Understand the phrase "the product of seven and the difference":
- The word 'product' indicates multiplication.
- We need to multiply 7 by the expression we obtained in the previous step, which is [tex]\( (x - 10) \)[/tex].

Combining these observations, the expression that represents "the product of seven and the difference between a number and ten" is:

[tex]\[ 7(x - 10) \][/tex]

### Checking the options:
A. [tex]\( 7(x - 10) \)[/tex] - This matches our derived expression.
B. [tex]\( 7x - 10 \)[/tex] - This is not accurate as it does not interpret the word "product" correctly.
C. [tex]\( 7(10 - x) \)[/tex] - This is incorrect because it reverses the terms inside the parenthesis.
D. [tex]\( 10 - 7x \)[/tex] - This does not match the word description at all.

### Conclusion:
The correct answer is option A: [tex]\( 7(x - 10) \)[/tex].
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