To solve the equation [tex]\( 3(n-9) - 2(n+4) = 6n \)[/tex], follow these steps:
1. Distribute the 3 and -2 on the left-hand side of the equation:
[tex]\[
3n - 27 - 2n - 8 = 6n
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
(3n - 2n) - 27 - 8 = 6n \implies n - 35 = 6n
\][/tex]
3. Isolate the variable [tex]\( n \)[/tex] by moving all terms involving [tex]\( n \)[/tex] to one side of the equation and constant terms to the opposite side:
[tex]\[
n - 6n = 35 \implies -5n = 35
\][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides of the equation by -5:
[tex]\[
n = \frac{35}{-5} \implies n = -7
\][/tex]
Thus, the solution to the equation is:
[tex]\[
n = -7
\][/tex]
