1. **Stating the problem:** Solve the equation $50 \tan x = 1$ for $x$. 2. **Rewrite the equation:** Divide both sides by 50 to isolate $\tan x$: $$\tan x = \frac{1}{50}$$ 3. **Recall the general solution for $\tan x = a$:** $$x = \arctan(a) + k\pi, \quad k \in \mathbb{Z}$$ because the tangent function has period $\pi$. 4. **Apply the formula:** $$x = \arctan\left(\frac{1}{50}\right) + k\pi$$ 5. **Interpretation:** The solution is all angles whose tangent is $\frac{1}{50}$, repeating every $\pi$ radians. **Final answer:** $$\boxed{x = \arctan\left(\frac{1}{50}\right) + k\pi, \quad k \in \mathbb{Z}}$$