1. **State the problem:** Solve the compound inequality $$2x + 5 \leq -6 \text{ or } 2x + 5 \geq 6$$. 2. **Understand the problem:** This is a compound inequality with an "or" condition, meaning the solution set includes values of $x$ that satisfy either inequality. 3. **Solve the first inequality:** $$2x + 5 \leq -6$$ Subtract 5 from both sides: $$2x + 5 - 5 \leq -6 - 5$$ $$2x \leq -11$$ Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} \leq \frac{-11}{2}$$ $$x \leq -\frac{11}{2}$$ 4. **Solve the second inequality:** $$2x + 5 \geq 6$$ Subtract 5 from both sides: $$2x + 5 - 5 \geq 6 - 5$$ $$2x \geq 1$$ Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} \geq \frac{1}{2}$$ $$x \geq \frac{1}{2}$$ 5. **Combine the solutions:** The solution set is all $x$ such that $$x \leq -\frac{11}{2} \text{ or } x \geq \frac{1}{2}$$ 6. **Final answer:** $$(-\infty, -\frac{11}{2}] \cup [\frac{1}{2}, \infty)$$ Note: The user provided solution set has $-\frac{11}{12}$ which appears to be a typo; the correct boundary is $-\frac{11}{2}$ based on the calculations above.