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 simplify each part step by step:

1. Distribute the constants:
- \(7(n−2) = 7n - 14\)
- \(5(n+4) = 5n + 20\)
- \(3(n+1) = 3n + 3\)

2. Combine all the expressions:
\[
7n - 14 + 5n + 20 + 3n + 3
\]

3. Combine like terms (the \(n\) terms and the constant terms):
- \(7n + 5n + 3n = 15n\)
- \(-14 + 20 + 3 = 9\)

4. Putting it all together gives us:
\[
15n + 9
\]

Thus, the final answer is **15n + 9**.

So the correct response is: **15n + 9**.