Answer :
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]
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]
