To determine which option best describes the algebraic expression [tex]\(15x + 8\)[/tex], let's break down the components of the expression step-by-step.
1. Algebraic Expression: [tex]\(15x + 8\)[/tex]
- Here, [tex]\(15x\)[/tex] means fifteen times a number [tex]\(x\)[/tex].
- The entire expression is the sum of [tex]\(15x\)[/tex] and [tex]\(8\)[/tex].
2. Detailed Breakdown:
- [tex]\(15x\)[/tex]: This is "fifteen times a number [tex]\(x\)[/tex]".
- [tex]\(+ 8\)[/tex]: This indicates that we are adding 8 to [tex]\(15x\)[/tex].
3. Analyzing Each Option:
- Option A: "Fifteen times the quantity of a number plus eight."
- This suggests we are taking a number, adding 8 to it first, and then multiplying by 15, which is written as [tex]\(15(x + 8)\)[/tex].
- Clearly, [tex]\(15(x + 8)\)[/tex] is not the same as [tex]\(15x + 8\)[/tex].
- Option B: "Fifteen times the sum of a number and eight."
- This also means we first add a number and eight, and then multiply the result by fifteen, giving [tex]\(15(x + 8)\)[/tex].
- Hence, [tex]\(15(x + 8)\)[/tex] is not equivalent to [tex]\(15x + 8\)[/tex].
- Option C: "The product of fifteen plus a number and eight."
- The phrase "the product of fifteen plus a number" and then "and eight" is ambiguous, but it seems to imply either multiplication or an incorrect order of operations.
- This does not sufficiently describe [tex]\(15x + 8\)[/tex].
- Option D: "The sum of fifteen times a number and eight."
- This correctly describes the given expression [tex]\(15x + 8\)[/tex].
- Here, we first calculate [tex]\(15x\)[/tex] (fifteen times a number [tex]\(x\)[/tex]) and then we add 8.
4. Conclusion:
- Option D accurately describes the algebraic expression [tex]\(15x + 8\)[/tex].
Therefore, the best description for the algebraic expression [tex]\(15x + 8\)[/tex] is Option D: The sum of fifteen times a number and eight.
