To determine which expression correctly represents the given phrase "seven times the sum of a number, [tex]\( n \)[/tex], and four," let's break down the phrase step by step.
1. Identifying the sum:
- We need to consider the sum of [tex]\( n \)[/tex] and 4, which is [tex]\( n + 4 \)[/tex].
2. Multiplying the sum:
- According to the phrase, this sum ([tex]\( n + 4 \)[/tex]) needs to be multiplied by seven.
- Mathematically, this can be represented by placing seven in front of the sum and using parentheses to indicate that we are multiplying the entire sum by seven: [tex]\( 7(n+4) \)[/tex].
Now, let's compare this to the given options:
A. [tex]\( 4(n+7) \)[/tex]:
- This option multiplies four by the sum of [tex]\( n \)[/tex] and seven, which does not match the phrase.
B. [tex]\( 7(n+4) \)[/tex]:
- This option multiplies seven by the sum of [tex]\( n \)[/tex] and four, which exactly represents the given phrase.
C. [tex]\( 7n+4 \)[/tex]:
- This option adds four to seven times [tex]\( n \)[/tex], which is not what the phrase describes.
D. [tex]\( n(4+7) \)[/tex]:
- This option multiplies [tex]\( n \)[/tex] by the sum of four and seven, which also does not match the phrase.
Therefore, the correct expression that represents "seven times the sum of a number, [tex]\( n \)[/tex], and four" is:
B. [tex]\( 7(n+4) \)[/tex]
