Solve for x in the equation 1/4x = 2 + 1/4.

To add 2 and $\frac{1}{4}$, we convert 2 to a fraction with a denominator of 4:

$$2 = \frac{2 \times 4}{4} = \frac{8}{4}$$

Now, add the fractions:

$$2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{8+1}{4} = \frac{9}{4}$$

So the equation becomes:

$$\frac{1}{4}x = \frac{9}{4}$$

To isolate $x$, multiply both sides of the equation by 4:

$$4 \times \frac{1}{4}x = 4 \times \frac{9}{4}$$ $$x = 9$$

The value of $x$ is $\boxed{\textbf{9}}$.