When $y$ varies inversely as $x$, it means that their product is constant. Mathematically, this can be expressed as:

$y \times x = k$

where $k$ is the constant of variation.

Given:

• $y = 9$ when $x = 2$

First, find the constant $k$:

$k = y \times x = 9 \times 2 = 18$

Now, use the constant $k$ to find $y$ when $x = 3$:

$y \times 3 = 18$

$y = \frac{18}{3} = 6$

So, $y = 6$ when $x = 3$.

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. If $y$ varies inversely as $x$ and $y = 4$ when $x = 5$, what is $y$ when $x = 10$?
2. Suppose $y$ varies inversely as $x$ and $y = 12$ when $x = 3$. Find the value of $y$ when $x = 6$.
3. If $y$ varies inversely as $x$ and the constant $k = 20$, what is $y$ when $x = 4$?
4. Given $y$ varies inversely as $x$ and $y = 8$ when $x = 2.5$, find $x$ when $y = 16$.
5. If $y$ varies inversely as $x$ and $x = 7$ when $y = 3$, what is the constant $k$?

Tip: When dealing with inverse variation problems, always start by finding the constant of variation $k$. This will make solving for any unknowns much easier.