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

Question

.(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