To solve the question, let's break down the word description step-by-step:
### Step-by-Step Solution:
1. Identify the main operation:
The phrase "The product of" indicates that multiplication is involved.
2. Separate the components involved in the multiplication:
The description specifies two components to multiply:
- The number "two"
- The "difference between a number and eleven"
3. Understand the "difference between a number and eleven":
Let's represent "a number" with the variable [tex]\( x \)[/tex]. The difference between [tex]\( x \)[/tex] and 11 is expressed as:
[tex]\[
x - 11
\][/tex]
4. Combine the components using multiplication:
Now, multiply "two" by the difference we found:
[tex]\[
2 \cdot (x - 11)
\][/tex]
### Conclusion:
When we convert the given word description into an algebraic expression, it translates to:
[tex]\[
2(x - 11)
\][/tex]
### Verification with Given Options:
- Option A: [tex]\( 11 - 2x \)[/tex] does not match the description, because it subtracts twice the number from 11.
- Option B: [tex]\( 2x - 11 \)[/tex] does not match the description, because it subtracts 11 from twice the number.
- Option C: [tex]\( 2(11 - x) \)[/tex] does not match the description, because it multiplies twice the difference of 11 and the number.
- Option D: [tex]\( 2(x - 11) \)[/tex] correctly matches the description as it multiplies two by the difference between the number and eleven.
Thus, the correct algebraic expression is [tex]\( 2(x - 11) \)[/tex], which corresponds to:
Option D: [tex]\( 2(x - 11) \)[/tex]
