1. **State the problem:** Solve the equation $$\frac{3x - 4}{4} = 5x - 1$$. 2. **Multiply both sides by 4** to eliminate the denominator: $$4 \times \frac{3x - 4}{4} = 4 \times (5x - 1)$$ 3. Simplify both sides: $$\cancel{4} \times \frac{3x - 4}{\cancel{4}} = 20x - 4$$ $$3x - 4 = 20x - 4$$ 4. **Subtract 3x from both sides** to get all $x$ terms on one side: $$3x - 4 - 3x = 20x - 4 - 3x$$ $$-4 = 17x - 4$$ 5. **Add 4 to both sides** to isolate the $x$ term: $$-4 + 4 = 17x - 4 + 4$$ $$0 = 17x$$ 6. **Divide both sides by 17** to solve for $x$: $$\frac{0}{17} = \frac{17x}{17}$$ $$0 = x$$ **Final answer:** $$x = 0$$