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What is the solution to this equation?

[tex]\[
3(n-9)-2(n+4)=6n
\][/tex]

[tex]\[
n= \square
\][/tex]



Answer :

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]