1. **State the problem:** Solve the inequality $4x - 1 < 12x - 11$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. When subtracting or adding terms, do the same on both sides. 3. **Step 1:** Subtract $4x$ from both sides: $$4x - 1 - 4x < 12x - 11 - 4x$$ which simplifies to $$-1 < 8x - 11$$ 4. **Step 2:** Add $11$ to both sides: $$-1 + 11 < 8x - 11 + 11$$ which simplifies to $$10 < 8x$$ 5. **Step 3:** Divide both sides by $8$ (positive number, so inequality direction stays the same): $$\frac{10}{8} < x$$ which simplifies to $$\frac{5}{4} < x$$ 6. **Final answer:** $$x > \frac{5}{4}$$ This means $x$ must be greater than $1.25$ to satisfy the inequality.