To solve for \( a \) in the equation 

\[
u = \frac{K}{a(w + v)},
\]

we can follow these steps:

1. **Multiply both sides by \( a(w + v) \):**
   \[
   u \cdot a(w + v) = K
   \]

2. **Isolate \( a \):**
   \[
   a(w + v) = \frac{K}{u}
   \]

3. **Divide both sides by \( w + v \) to solve for \( a \):**
   \[
   a = \frac{K}{u(w + v)}
   \]

So, the solution for \( a \) is:

\[
a = \frac{K}{u(w + v)}
\]

Would you like to explore further details or need additional explanations?

Here are some related questions:

1. How does the value of \( a \) change if \( u \) increases?
2. What happens to \( a \) if \( w + v \) becomes very large?
3. Can you solve for \( w \) instead, and how would that affect the interpretation?
4. If \( K \) is doubled, how does \( a \) change?
5. What is the impact on \( a \) if \( u \) approaches zero?
6. How can you check the correctness of your solution for \( a \)?
7. What are the implications if \( a \) is negative?
8. How does this equation relate to proportional relationships in mathematics?

**Tip:** When isolating variables in an equation, ensure that each step you take is mathematically equivalent to the previous form of the equation. This maintains the equality throughout your calculations.

Learn how to solve for a in the equation nu = K / (a(w + v)) with a step-by-step solution. This problem involves algebraic manipulation and isolation of variables. Suitable for high school students.

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