To determine the correct algebraic expression for the given word description, let's break it down step by step:
1. Identify the Components:
- "The product of two" indicates that 2 is being multiplied by something.
- "The difference between a number and eleven" describes a subtraction operation where we take a number (let's call it [tex]\( x \)[/tex]) and subtract 11 from it.
2. Construct the Expression:
- The difference between a number [tex]\( x \)[/tex] and eleven is written as [tex]\( x - 11 \)[/tex].
- The product of 2 and this difference means we need to multiply 2 by [tex]\( (x - 11) \)[/tex].
The resulting expression is [tex]\( 2(x - 11) \)[/tex].
3. Match with Given Options:
- Option A: [tex]\( 11 - 2x \)[/tex] (Incorrect: this represents subtracting twice the number from 11)
- Option B: [tex]\( 2(x - 11) \)[/tex] (Correct: this matches our derived expression)
- Option C: [tex]\( 2x - 11 \)[/tex] (Incorrect: this represents twice the number minus 11)
- Option D: [tex]\( 2(11 - x) \)[/tex] (Incorrect: this represents the product of 2 and the difference between 11 and the number, which is the reverse order)
Thus, the algebraic expression that represents the word description "The product of two and the difference between a number and eleven" is:
[tex]\[ \boxed{2(x - 11)} \][/tex]
