To determine which algebraic expression matches the description, we need to carefully translate the words into mathematical terms:
1. Identify key phrases in the description:
- "The product of nine": This tells us we will multiply by 9.
- "The difference between a number and five": This indicates we will subtract 5 from a variable, typically represented by [tex]\( x \)[/tex].
2. Translate the description into an expression:
- The difference between a number [tex]\( x \)[/tex] and five is [tex]\( x - 5 \)[/tex].
- The product of nine and this difference is [tex]\( 9 \cdot (x - 5) \)[/tex].
3. Review the given options to find a match:
A. [tex]\( 9(x - 5) \)[/tex] matches exactly with our translated expression.
B. [tex]\( 5 - 9x \)[/tex] represents five decreased by nine times a number, which does not match the description.
C. [tex]\( 9x - 5 \)[/tex] represents nine times a number decreased by five, which does not match the description.
D. [tex]\( 9(5 - x) \)[/tex] represents nine times the difference between five and a number, which does not match the description.
The correct algebraic expression that matches the description is:
A. [tex]\( 9(x - 5) \)[/tex]
