Solve the literal equation for $n$. Simplify your answer.
$k=\frac{-2 m-3}{n p}$
Answer (2)
Multiply both sides of the equation by n p : kn p = − 2 m − 3 .
Divide both sides of the equation by k p : n = k p − 2 m − 3 .
Simplify the expression: n = k p − 2 m − 3 .
The solution for n is: n = k p − 2 m − 3 .
Explanation
Understanding the Problem We are given the equation k = n p − 2 m − 3 and we want to solve for n . This means we want to isolate n on one side of the equation.
Multiplying by np First, multiply both sides of the equation by n p to get rid of the fraction: k p = n p − 2 m − 3 p k p = − 2 m − 3
Dividing by kp Next, divide both sides of the equation by k p to isolate n :
k p k p = k p − 2 m − 3 n = k p − 2 m − 3
Final Answer The solution is n = k p − 2 m − 3 .
Examples
Literal equations are useful in physics and engineering when you want to rearrange a formula to solve for a different variable. For example, the equation for the force due to gravity is F = G r 2 m 1 m 2 . If you wanted to solve for the distance r between two objects given the force F , you would rearrange the equation to isolate r . This is a literal equation because you are manipulating variables rather than numbers.
To solve for n in the equation k = n p − 2 m − 3 , we multiply both sides by n p and then divide by k p , resulting in n = k p − 2 m − 3 . This rearrangement allows us to express n in terms of the other variables. The final answer is n = k p − 2 m − 3 .
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