To solve the equation [tex]\(3(n - 9) - 2(n + 4) = 6n\)[/tex], follow these steps:
1. Distribute the coefficients through the parentheses:
[tex]\[
3(n - 9) - 2(n + 4) = 6n
\][/tex]
[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. Subtract [tex]\(n\)[/tex] from both sides to get all the [tex]\(n\)[/tex] terms on one side of the equation:
[tex]\[
-35 = 6n - n
\][/tex]
[tex]\[
-35 = 5n
\][/tex]
4. Divide both sides by 5 to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \frac{-35}{5}
\][/tex]
[tex]\[
n = -7
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
n = -7
\][/tex]
