If x is inversely proportional to y, then we can write the relationship between x and y as \(x = \frac{k}{y}\), where k is the constant of proportionality. We can find the value of k by using the given information that x = 2\(\frac{1}{2}\) when y = 2.

Substituting these values into the equation, we get \(2\frac{1}{2} = \frac{k}{2}\), which simplifies to \(k = 5\).

Now that we know the value of k, we can use it to find the value of x when y = 4. Substituting these values into the equation, we get \(x = \frac{5}{4}\), which simplifies to \(x = 1\frac{1}{4}\).