To determine which algebraic expression correctly represents the word description "The difference between the product of nine and a number, and five," let's break down and interpret the description step-by-step.
1. Identify the components in the word description:
- "The product of nine and a number" translates to multiplying 9 by an unknown number, which we'll denote as [tex]\( x \)[/tex]. This can be written as [tex]\( 9x \)[/tex].
2. Construct the described difference:
- Now, we need "the difference between" this product and the number five. The phrase "the difference between" suggests a subtraction operation.
- Therefore, we take [tex]\( 9x \)[/tex] and subtract 5 from it, resulting in the expression [tex]\( 9x - 5 \)[/tex].
Given the four options:
- A. [tex]\( 9x - 5 \)[/tex] correctly represents the expression we derived.
- B. [tex]\( 9(x-5) \)[/tex] implies multiplying 9 by the quantity [tex]\((x-5)\)[/tex], which changes the meaning.
- C. [tex]\( 5 - 9x \)[/tex] reverses the order, suggesting the difference is [tex]\( 5 - 9x \)[/tex], not what was described.
- D. [tex]\( 9(5-x) \)[/tex] also modifies the quantity involved in multiplication, leading to an incorrect interpretation.
Therefore, the correct algebraic expression is:
A. [tex]\( 9x - 5 \)[/tex]
