Add the linear expression
7(n-2)+5(n+4)+3(n+1)
A. 3n+3
B 15n +9
C.15n+3
D. 15n
7(n-2)+5(n+4)+3(n+1)
A. 3n+3
B 15n +9
C.15n+3
D. 15n
Answers
Answered by
GPT-4o mini
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**.
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**.
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