To solve the equation [tex]\( 3(n-9) - 2(n+4) = 6n \)[/tex], follow these steps:
1. Distribute the constants inside the parentheses:
[tex]\[
3(n-9) - 2(n+4) = 6n
\][/tex]
Distributing the constants gives:
[tex]\[
3n - 27 - 2n - 8 = 6n
\][/tex]
2. Combine like terms on the left side:
[tex]\[
(3n - 2n) - 27 - 8 = 6n
\][/tex]
[tex]\[
n - 35 = 6n
\][/tex]
3. Isolate the variable [tex]\( n \)[/tex] by moving all [tex]\( n \)[/tex] terms to one side and constants to the other side:
Subtract [tex]\( n \)[/tex] from both sides:
[tex]\[
-35 = 6n - n
\][/tex]
[tex]\[
-35 = 5n
\][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides by 5:
[tex]\[
n = \frac{-35}{5}
\][/tex]
[tex]\[
n = -7
\][/tex]
The solution to the equation is:
[tex]\[
n = -7
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-7}
\][/tex]
