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