Make n the subject: [tex]
\begin{array}{l}
b n-w=f \\
n=(f+w) b
\end{array}
[/tex]
Answer (1)
Add w to both sides of the equation: bn = f + w .
Divide both sides by b : n = b f + w .
The correct expression for n is n = b f + w .
Explanation
Understanding the Problem We are given the equation bn − w = f and asked to make n the subject. This means we want to isolate n on one side of the equation. The provided solution n = ( f + w ) b is incorrect, so we need to derive the correct expression for n .
Isolating the term with n To isolate n , we first add w to both sides of the equation: bn − w + w = f + w bn = f + w
Solving for n Next, we divide both sides of the equation by b (assuming b e q 0 ): b bn = b f + w n = b f + w
Final Answer Therefore, the correct expression for n is b f + w .
Examples
In physics, this type of equation can represent forces or energies. For example, if b is the distance, n is the force, w is the initial energy, and f is the final energy, then the equation bn − w = f relates these quantities. Solving for n allows you to determine the force required to change the energy from w to f over a distance b . This is useful in mechanics problems where you need to calculate the force applied to an object.
