Add the linear expressions: 7(n−2)+5(n+4)+3(n+1)

Question

.(1 point)
Responses

3n+3
3 n plus 3

15n+3
15 n plus 3

15n
15 n

15n+9

Answer 1

To add the linear expressions \( 7(n−2) + 5(n+4) + 3(n+1) \), we first expand each term:

1. Expand \( 7(n−2) \): \[ 7(n−2) = 7n - 14 \]

2. Expand \( 5(n+4) \): \[ 5(n+4) = 5n + 20 \]

3. Expand \( 3(n+1) \): \[ 3(n+1) = 3n + 3 \]

Now, we combine all these expanded terms: \[ 7n - 14 + 5n + 20 + 3n + 3 \]

Next, we combine the like terms (the terms with \( n \) and the constant terms):

• For the \( n \) terms: \[ 7n + 5n + 3n = 15n \]

• For the constant terms: \[ -14 + 20 + 3 = 9 \]

Putting it all together, we get: \[ 15n + 9 \]

Thus, the final result is: \[ \boxed{15n+9} \]