1. **State the problem:** Solve the inequality $2x - 3 > 1$. 2. **Write the inequality:** $$2x - 3 > 1$$ 3. **Add 3 to both sides to isolate the term with $x$:** $$2x - 3 + 3 > 1 + 3$$ $$2x > 4$$ 4. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{2} > \frac{4}{2}$$ $$x > 2$$ 5. **Interpretation:** The solution to the inequality is all values of $x$ greater than 2. 6. **Graph explanation:** The line $y = 2x - 3$ crosses the y-axis at $-3$ and has a slope of 2. The shaded region above the line represents all points where $y > 2x - 3$. Since the inequality is $2x - 3 > 1$, this corresponds to $x > 2$ on the x-axis. **Final answer:** $$x > 2$$