To solve the equation [tex]\(12n + 7p - 6n = 25p\)[/tex] for [tex]\(n\)[/tex], follow these steps:
1. Combine like terms on the left-hand side of the equation:
[tex]\[
(12n - 6n) + 7p = 25p
\][/tex]
Simplify [tex]\(12n - 6n\)[/tex]:
[tex]\[
6n + 7p = 25p
\][/tex]
2. Isolate the term involving [tex]\(n\)[/tex] by moving the term [tex]\(7p\)[/tex] to the right-hand side of the equation. Do this by subtracting [tex]\(7p\)[/tex] from both sides:
[tex]\[
6n + 7p - 7p = 25p - 7p
\][/tex]
This simplifies to:
[tex]\[
6n = 18p
\][/tex]
3. Solve for [tex]\(n\)[/tex] by dividing both sides of the equation by 6:
[tex]\[
n = \frac{18p}{6}
\][/tex]
Simplify the right-hand side:
[tex]\[
n = 3p
\][/tex]
Hence, the solution to the equation is:
[tex]\[
n = 3p
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{n = 3p} \text{ (Option C)}
\][/tex]
