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

To add the linear expressions \(7(n−2)+5(n+4)+3(n+1)\), 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).