1. **State the problem:** Solve the inequality $3x - 5 > 1$ for $x$. 2. **Write the inequality:** $$3x - 5 > 1$$ 3. **Add 5 to both sides to isolate the term with $x$:** $$3x - 5 + 5 > 1 + 5$$ $$3x > 6$$ 4. **Divide both sides by 3 to solve for $x$:** $$\frac{\cancel{3}x}{\cancel{3}} > \frac{6}{3}$$ $$x > 2$$ 5. **Interpretation:** The solution is all real numbers greater than 2. **Final answer:** $$x > 2$$