To find the algebraic expression that represents the given word description, let's break it down step by step:
1. Understand the terminology:
- "The product of two": This indicates multiplication involving the number 2.
- "The difference between a number and eleven": Choose a variable, let's denote this number as [tex]\( x \)[/tex]. The difference between [tex]\( x \)[/tex] and 11 is written as [tex]\( x - 11 \)[/tex].
2. Combine the terms:
- According to the word description, we need to find the product of 2 and the difference between [tex]\( x \)[/tex] and 11. In algebraic terms, this can be written as:
[tex]\[
2 \times (x - 11)
\][/tex]
3. Simplification:
- There is no further simplification needed for this expression; it is already in its simplest form.
4. Match with the options:
- Compare this expression to the provided multiple-choice options:
[tex]\[
\text{A. } 2(x - 11)
\][/tex]
[tex]\[
\text{B. } 11 - 2x
\][/tex]
[tex]\[
\text{C. } 2(11 - x)
\][/tex]
[tex]\[
\text{D. } 2x - 11
\][/tex]
- The expression [tex]\( 2(x - 11) \)[/tex] matches perfectly with option A.
Therefore, the correct algebraic expression representing the word description "The product of two and the difference between a number and eleven" is:
[tex]\[
\boxed{2(x - 11)}
\][/tex]
The correct answer is A. [tex]\( 2(x - 11) \)[/tex].
