1. **State the problem:** Find the range of the function $$f(x) = \frac{12x + 5}{6x}$$. 2. **Rewrite the function:** Simplify the expression by dividing each term in the numerator by the denominator: $$f(x) = \frac{12x}{6x} + \frac{5}{6x}$$ 3. **Simplify terms:** $$f(x) = 2 + \frac{5}{6x}$$ 4. **Analyze the function:** The function is defined for all real numbers except where the denominator is zero, i.e., $$x \neq 0$$. 5. **Find the range:** Let $$y = 2 + \frac{5}{6x}$$. 6. **Solve for $$x$$ in terms of $$y$$:** $$y - 2 = \frac{5}{6x}$$ 7. **Invert the equation:** $$6x = \frac{5}{y - 2}$$ 8. **Solve for $$x$$:** $$x = \frac{5}{6(y - 2)}$$ 9. **Domain restriction for $$x$$:** Since $$x$$ cannot be zero, set $$x \neq 0$$: $$\frac{5}{6(y - 2)} \neq 0$$ 10. **This is true for all $$y$$ except when denominator is zero:** $$y - 2 \neq 0 \implies y \neq 2$$ 11. **Conclusion:** The function can take all real values except $$y = 2$$. **Final answer:** $$\boxed{\text{Range} = (-\infty, 2) \cup (2, \infty)}$$