Answer:
The correct way to write \( w \) is:
\[ w = v - \frac{z}{k} \frac{x}{y} \]
Step-by-step explanation:
To rewrite the equation \( \frac{x}{y} = k \frac{v - w}{z} \) to solve for \( w \), we need to isolate \( w \) on one side of the equation.
1. **Multiply both sides by \( z \)**:
\[ z \frac{x}{y} = k(v - w) \]
2. **Divide both sides by \( k \)**:
\[ \frac{z}{k} \frac{x}{y} = v - w \]
3. **Subtract \( v \) from both sides**:
\[ \frac{z}{k} \frac{x}{y} - v = -w \]
4. **Multiply both sides by \( -1 \)**:
\[ w = -\left(\frac{z}{k} \frac{x}{y} - v\right) \]
So, the correct way to write \( w \) is:
\[ w = v - \frac{z}{k} \frac{x}{y} \]
