To determine the equation that correctly expresses [tex]\( n \)[/tex] in terms of [tex]\( p \)[/tex] given the equation [tex]\( p = \frac{2}{n} + 3 \)[/tex], follow the steps below:
1. Isolate the term containing [tex]\( n \)[/tex]:
[tex]\[
p = \frac{2}{n} + 3
\][/tex]
Subtract 3 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
p - 3 = \frac{2}{n}
\][/tex]
2. Solve for [tex]\( n \)[/tex]:
We need to express [tex]\( n \)[/tex] in terms of [tex]\( p \)[/tex]. To do this, take the reciprocal of both sides:
[tex]\[
\frac{1}{p - 3} = \frac{n}{2}
\][/tex]
Then, multiply both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{2}{p - 3}
\][/tex]
Therefore, the equation that correctly expresses [tex]\( n \)[/tex] in terms of [tex]\( p \)[/tex] is:
[tex]\[
n = \frac{2}{p - 3}
\][/tex]
Thus, the correct answer is option C: [tex]\( n = \frac{2}{p - 3} \)[/tex].
