Since y is inversely proportional to x, we can write the relationship between x and y as:

\(y = \frac{k}{x}\),

where k is the constant of proportionality.

We can find the value of k by using the given information that y = 4 when x = 1/2.

Substituting these values into the equation \(y = \frac{k}{x}\), we get:

\(4 = \frac{k}{\frac{1}{2}}\), which gives us k = 2.

Therefore, the equation that describes the relationship between x and y is \(y = \frac{2}{x}\).

Now, we can use this equation to find the value of x when y = 10.

Substituting y = 10 into the equation \(y = \frac{2}{x}\), we get \(10 = \frac{2}{x}\).

\(x = \frac{2}{10} = \frac{1}{5}\).