Let's solve the equation step-by-step.
Given:
[tex]\[ 3(n-9) - 2(n+4) = 6n \][/tex]
1. Distribute the constants inside the parentheses:
[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 the [tex]\( n \)[/tex] term to the right side:
[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]
So, the solution to the equation is:
[tex]\[ n = -7 \][/tex]
