Question

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

15n
15 n

3n+3
3 n plus 3

15n+9
15 n plus 9

15n+3

Answer 1

To add the linear expressions \(7(n−2)+5(n+4)+3(n+1)\), let's first distribute the constants across the parentheses:

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

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

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

Now, we can combine all these results:

\[
7n - 14 + 5n + 20 + 3n + 3
\]

Next, we'll combine the \(n\) terms and the constant terms separately:

- Combine \(n\) terms:
\[
7n + 5n + 3n = 15n
\]

- Combine constant terms:
\[
-14 + 20 + 3 = 9
\]

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

Thus, the answer is:

**15n + 9**