Question

Add the linear expressions: 7(n−2)+5(n+4)+3(n+1)
.(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:
\[
\boxed{15n+9}
\]