1. **State the problem:** Solve the inequality $$\frac{x}{9} - \frac{x}{7} < 0$$. 2. **Find a common denominator:** The denominators are 9 and 7, so the common denominator is $$63$$. 3. **Rewrite each fraction with denominator 63:** $$\frac{x}{9} = \frac{7x}{63}$$ $$\frac{x}{7} = \frac{9x}{63}$$ 4. **Rewrite the inequality:** $$\frac{7x}{63} - \frac{9x}{63} < 0$$ 5. **Combine the fractions:** $$\frac{7x - 9x}{63} < 0$$ 6. **Simplify the numerator:** $$\frac{-2x}{63} < 0$$ 7. **Since 63 is positive, multiply both sides by 63 (no sign change):** $$-2x < 0$$ 8. **Divide both sides by -2, remembering to flip the inequality sign because dividing by a negative:** $$\cancel{-2}x > \cancel{-2}0$$ $$x > 0$$ **Final answer:** $$x > 0$$