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What is the solution to this equation?
[tex]\[
\begin{array}{l}
3(n-9)-2(n+4)=6n \\
n=\square
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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