1. **State the problem:** Solve the inequality $2x - 1 < 9$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. Adding or subtracting the same number on both sides keeps the inequality direction the same. 3. **Add 1 to both sides:** $$2x - 1 + 1 < 9 + 1$$ $$2x < 10$$ 4. **Divide both sides by 2:** Since 2 is positive, the inequality direction stays the same. $$\frac{2x}{2} < \frac{10}{2}$$ $$x < 5$$ 5. **Final answer:** $$x < 5$$ This means all values of $x$ less than 5 satisfy the inequality.