1. **State the problem:** Solve the inequality $$\frac{x}{9} - \frac{x}{7} < 0$$ and determine which option about $x$ is correct. 2. **Find a common denominator:** The denominators are 9 and 7, so the common denominator is 63. 3. **Rewrite the inequality with common denominator:** $$\frac{7x}{63} - \frac{9x}{63} < 0$$ 4. **Combine the fractions:** $$\frac{7x - 9x}{63} < 0$$ $$\frac{-2x}{63} < 0$$ 5. **Simplify the inequality:** Since 63 is positive, multiply both sides by 63 without changing the inequality sign: $$-2x < 0$$ 6. **Divide both sides by -2:** Dividing by a negative number reverses the inequality sign: $$\cancel{-2}x \; \cancel{<} \; 0 \Rightarrow x > 0$$ 7. **Conclusion:** The solution to the inequality is $$x > 0$$. **Answer:** The correct option is **x > 0**.