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Sagot :
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].
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].
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