1. **State the problem:** We need to find which number among -2, -1, 0, and 1 satisfies the inequality $$5(2x - 3) > 3(2x - 4)$$. 2. **Write the inequality:** $$5(2x - 3) > 3(2x - 4)$$ 3. **Expand both sides:** $$10x - 15 > 6x - 12$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$10x - 6x > -12 + 15$$ 5. **Simplify both sides:** $$4x > 3$$ 6. **Divide both sides by 4:** $$\cancel{4}x > \cancel{4} \frac{3}{4}$$ $$x > \frac{3}{4}$$ 7. **Interpret the solution:** The inequality holds for all $x$ greater than $\frac{3}{4}$. 8. **Check the options:** - A. $-2$ (No, because $-2 < \frac{3}{4}$) - B. $-1$ (No, because $-1 < \frac{3}{4}$) - C. $0$ (No, because $0 < \frac{3}{4}$) - D. $1$ (Yes, because $1 > \frac{3}{4}$) **Final answer:** D. 1