To find the algebraic expression that represents the given word description, we break down the description into its components.
1. Phrase Analysis:
- The word "product" indicates multiplication.
- "Nine" suggests the multiplier is 9.
- "Difference between a number and five" suggests we are subtracting 5 from a variable number (let's call this number [tex]\( x \)[/tex]).
2. Translation to Algebraic Expression:
- The phrase "the difference between a number and five" translates to [tex]\( (x - 5) \)[/tex].
- The phrase "the product of nine and the difference" translates to multiplying 9 with the expression [tex]\( (x - 5) \)[/tex].
Putting these parts together, we get:
[tex]\[
9(x - 5)
\][/tex]
3. Justification:
- Option A: [tex]\( 9x - 5 \)[/tex] does not represent "the product of nine and the difference between a number and five." It implies nine times the number minus five, which is incorrect.
- Option B: [tex]\( 9(5 - x) \)[/tex] represents the product of nine and the difference between five and a number, which is not the same as “a number and five.”
- Option C: [tex]\( 9(x - 5) \)[/tex] correctly follows the description, as it multiplies nine by the difference between a number and five.
- Option D: [tex]\( 5 - 9x \)[/tex] incorrectly implies five minus the product of nine and the number.
Therefore, the correct algebraic expression is [tex]\( 9(x - 5) \)[/tex], which corresponds to option C.
So, the correct answer is:
C. \[tex]$9(x - 5)$[/tex]
