Solve $13 n-6 p-11 n=2 p$ for $n$
A. $n=-\frac{p}{2}$
B. $n=\frac{p}{4}$
C. $n=-2 p$
D. $n=4 p
Answer (2)
Combine like terms: 13 n − 11 n − 6 p = 2 n − 6 p .
Add 6 p to both sides: 2 n = 8 p .
Divide by 2: n = 4 p .
The solution is n = 4 p .
Explanation
Understanding the Problem We are given the equation 13 n − 6 p − 11 n = 2 p and asked to solve for n . This involves combining like terms and isolating n on one side of the equation.
Combining Like Terms First, we combine the n terms on the left side of the equation: 13 n − 11 n − 6 p = 2 p which simplifies to 2 n − 6 p = 2 p .
Isolating the n Term Next, we want to isolate the term with n . To do this, we add 6 p to both sides of the equation: 2 n − 6 p + 6 p = 2 p + 6 p which simplifies to 2 n = 8 p .
Solving for n Finally, to solve for n , we divide both sides of the equation by 2: 2 2 n = 2 8 p which simplifies to n = 4 p .
Final Answer Therefore, the solution is n = 4 p . Comparing this to the answer choices, we see that it matches option D.
Examples
Understanding how to solve for a variable in terms of another is useful in many real-world scenarios. For example, if you are a freelancer and your income ( n ) depends on the number of hours you work ( p ), the equation n = 4 p tells you that you earn $4 per hour. This allows you to easily calculate your earnings based on the number of hours you've worked, or conversely, determine how many hours you need to work to reach a specific income goal. This kind of algebraic manipulation is fundamental in personal finance, business, and many other fields.
The solution to the equation 13 n − 6 p − 11 n = 2 p is n = 4 p . This matches option D from the provided answer choices. Thus, the answer is confirmed as option D: n = 4 p .
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