If $y$ is one-fifth the value of $z$, then $y = \frac{1}{5}z = \frac{1}{5}(60) = 12$.
If $x$ is one-half the value of $y$, then $x = \frac{1}{2}y = \frac{1}{2}(12) = \boxed{6}$.
The answer is: 6
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The value of $x$ is one-half the value of $y$, and the value of $y$ is one-fifth the value of $z$. If $z$ is 60, what is the value of $x$?

### Answer:
