1. **State the problem:** Solve the system of inequalities: $$9 - 3x < 3$$ $$5 - 3x \geq -13$$ 2. **Solve the first inequality:** $$9 - 3x < 3$$ Subtract 9 from both sides: $$-3x < 3 - 9$$ $$-3x < -6$$ Divide both sides by -3 (remember to reverse the inequality sign): $$x > 2$$ 3. **Solve the second inequality:** $$5 - 3x \geq -13$$ Subtract 5 from both sides: $$-3x \geq -13 - 5$$ $$-3x \geq -18$$ Divide both sides by -3 (reverse the inequality sign): $$x \leq 6$$ 4. **Combine the solutions:** From the first inequality, $x > 2$. From the second inequality, $x \leq 6$. Therefore, the solution set is: $$2 < x \leq 6$$ This means $x$ is greater than 2 and less than or equal to 6.