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Add the linear expression

7(n-2)+5(n+4)+3(n+1)
A. 3n+3
B 15n +9
C.15n+3
D. 15n

1 answer

To simplify the expression \( 7(n-2) + 5(n+4) + 3(n+1) \), we will first distribute the coefficients in front of the parentheses:

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

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

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

Now combine all the distributed terms together: \[ 7n - 14 + 5n + 20 + 3n + 3 \]

Next, we will combine like terms (the \( n \) terms and the constant terms):

  • Combine \( n \) terms: \[ 7n + 5n + 3n = 15n \]
  • Combine constant terms: \[ -14 + 20 + 3 = 9 \]

Putting it all together, we have: \[ 15n + 9 \]

Thus, the final answer is \( 15n + 9 \), which corresponds to option B.