Question

which phrase is a description of $2(n + 7)$?
a 7 more than the product of 2 and n
b 7 more than the quotient of 2 and n
c 2 times the sum of n and 7
d 2 more than 7 more than n

Explanation:

Step1: Analyze the expression \(2(n + 7)\)

The parentheses indicate the sum of \(n\) and \(7\), so \(n + 7\) is "the sum of \(n\) and \(7\)".

Step2: Analyze the coefficient 2

The 2 outside the parentheses means we are multiplying the sum (\(n + 7\)) by 2, so this is "2 times the sum of \(n\) and \(7\)".

Step3: Evaluate the options

• Option A: "7 more than the product of 2 and \(n\)" would be \(2n + 7\), not \(2(n + 7)\).
• Option B: "7 more than the quotient of 2 and \(n\)" would be \(\frac{2}{n}+7\), which is not the given expression.
• Option C: Matches our analysis of \(2(n + 7)\) as "2 times the sum of \(n\) and 7".
• Option D: "2 more than 7 more than \(n\)" would be \(n + 7+ 2=n + 9\), not the given expression.

Answer:

C. 2 times the sum of n and 7