1. **State the problem:** Solve the inequality $4x - 1 < 12x - 1$. 2. **Write the inequality:** $$4x - 1 < 12x - 1$$ 3. **Add 1 to both sides to eliminate $-1$:** $$4x - 1 + 1 < 12x - 1 + 1$$ $$4x < 12x$$ 4. **Subtract $4x$ from both sides to isolate terms with $x$ on one side:** $$4x - 4x < 12x - 4x$$ $$0 < 8x$$ 5. **Divide both sides by 8 (positive number, so inequality direction stays the same):** $$\frac{0}{8} < \frac{8x}{8}$$ $$0 < x$$ 6. **Interpretation:** The solution to the inequality is all $x$ such that $x > 0$. **Final answer:** $$x > 0$$