1. **State the problem:** Simplify the expression $$\frac{4 \sin 30^\circ - \tan 45^\circ}{2 \cos 30^\circ}$$ and express it in the form $$\tan x$$ where $$x$$ is an acute angle. 2. **Recall the values of trigonometric functions:** - $$\sin 30^\circ = \frac{1}{2}$$ - $$\tan 45^\circ = 1$$ - $$\cos 30^\circ = \frac{\sqrt{3}}{2}$$ 3. **Substitute these values into the expression:** $$\frac{4 \times \frac{1}{2} - 1}{2 \times \frac{\sqrt{3}}{2}} = \frac{2 - 1}{\cancel{2} \times \frac{\sqrt{3}}{\cancel{2}}} = \frac{1}{\sqrt{3}}$$ 4. **Simplify the denominator:** $$\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ (rationalizing the denominator) 5. **Identify the angle $$x$$ such that $$\tan x = \frac{\sqrt{3}}{3}$$:** From trigonometric tables, $$\tan 30^\circ = \frac{\sqrt{3}}{3}$$. 6. **Conclusion:** The expression simplifies to $$\tan 30^\circ$$, so $$x = 30^\circ$$, which is an acute angle. **Final answer:** $$\boxed{\tan 30^\circ}$$