Solve [tex][tex]$12n + 7p - 6n = 25p$[/tex][/tex] for [tex][tex]$n$[/tex][/tex].

A. [tex][tex]$n = 6p$[/tex][/tex]
B. [tex][tex]$n = \frac{p}{6}$[/tex][/tex]
C. [tex][tex]$n = 3p$[/tex][/tex]
D. [tex][tex]$n = \frac{p}{3}$[/tex][/tex]



Answer :

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]