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].
