1. **State the problem:** Solve the compound inequality $-3x \leq -9$ or $3x - 26 \geq -8$. 2. **Solve the first inequality:** $$-3x \leq -9$$ Divide both sides by $-3$ and reverse the inequality sign because dividing by a negative number reverses the inequality: $$x \geq \cancel{-3} \frac{-9}{\cancel{-3}} = 3$$ 3. **Solve the second inequality:** $$3x - 26 \geq -8$$ Add 26 to both sides: $$3x \geq -8 + 26$$ $$3x \geq 18$$ Divide both sides by 3: $$x \geq \cancel{3} \frac{18}{\cancel{3}} = 6$$ 4. **Combine the solutions:** The compound inequality uses "or," so the solution is: $$x \geq 3 \quad \text{or} \quad x \geq 6$$ Since $x \geq 3$ already includes all values $x \geq 6$, the solution simplifies to: $$x \geq 3$$ 5. **Interpretation:** On the number line, this means all values from 3 to infinity satisfy the compound inequality. **Final answer:** $$\boxed{x \geq 3}$$