Question

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

15n+3
15 n plus 3

15n
15 n

15n+9
15 n plus 9

3n+3

Answer 1

To add the linear expressions \(7(n−2)+5(n+4)+3(n+1)\), we will first distribute the numbers outside the parentheses to the terms inside the parentheses:

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

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

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

Now, we can combine all these results:
\[
7(n - 2) + 5(n + 4) + 3(n + 1) = (7n - 14) + (5n + 20) + (3n + 3)
\]

Next, we will combine like terms:
- Combine the \(n\) terms:
\[
7n + 5n + 3n = 15n
\]

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

Putting it all together:
\[
7(n - 2) + 5(n + 4) + 3(n + 1) = 15n + 9
\]

So, the final answer is:
\[
\boxed{15n + 9}
\]

Among your responses, the correct one is:
**15n+9** (15 n plus 9).