To solve the equation [tex]\( 3(n - 9) - 2(n + 4) = 6n \)[/tex], follow these steps:
1. Distribute the constants on both sides:
- For the term [tex]\( 3(n - 9) \)[/tex]:
[tex]\[
3(n - 9) = 3n - 27
\][/tex]
- For the term [tex]\( -2(n + 4) \)[/tex]:
[tex]\[
-2(n + 4) = -2n - 8
\][/tex]
2. Rewrite the equation with the distributed terms:
[tex]\[
3n - 27 - 2n - 8 = 6n
\][/tex]
3. Combine like terms on the left side:
- Combine the [tex]\( n \)[/tex] terms:
[tex]\[
3n - 2n = n
\][/tex]
- Combine the constants:
[tex]\[
-27 - 8 = -35
\][/tex]
- So, the equation now looks like:
[tex]\[
n - 35 = 6n
\][/tex]
4. Move all terms involving [tex]\( n \)[/tex] to one side of the equation:
[tex]\[
n - 6n = 35
\][/tex]
Simplify the terms:
[tex]\[
-5n = 35
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{35}{-5}
\][/tex]
[tex]\[
n = -7
\][/tex]
Therefore, the value of [tex]\( n \)[/tex] is [tex]\( -7 \)[/tex].
[tex]\[
n = -7
\][/tex]
