To solve for \( w \) in terms of \( u \) and \( v \), let's start with the equation you previously provided:

\[
x = \frac{1}{v \cdot u \cdot w}
\]

First, rearrange the equation to solve for \( w \):

### Steps:

1. Start with the original equation:

\[
x = \frac{1}{v \cdot u \cdot w}
\]

2. Multiply both sides by \( v \cdot u \cdot w \) to eliminate the fraction:

\[
x \cdot v \cdot u \cdot w = 1
\]

3. Divide both sides by \( x \cdot v \cdot u \):

\[
w = \frac{1}{x \cdot v \cdot u}
\]

Now you have the equation for \( w \) in terms of \( u \) and \( v \):

\[
w = \frac{1}{x \cdot v \cdot u}
\]

This equation expresses \( w \) in terms of \( u \), \( v \), and \( x \).

Would you like more details or have any questions about this?

Here are some related questions to explore:

1. How would you solve for \( x \) in terms of \( u \), \( v \), and \( w \)?
2. If \( u = 2 \), \( v = 3 \), and \( x = 4 \), what is the value of

This guide demonstrates how to solve for w in terms of u and v using algebraic manipulation. The step-by-step solution involves rearranging a rational equation and applying properties of equality. Suitable for high school students, this problem introduces key algebra concepts.

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