Absolute Inequality 93069F

1. **State the problem:** Solve the inequality $$\lvert x+10 \rvert > 5$$. 2. **Recall the definition of absolute value inequality:** For $$\lvert A \rvert > B$$ where $$B > 0$$, the solution is $$A < -B$$ or $$A > B$$. 3. **Apply the rule:** Here, $$A = x+10$$ and $$B = 5$$, so $$x+10 < -5 \quad \text{or} \quad x+10 > 5$$ 4. **Solve each inequality separately:** - For $$x+10 < -5$$: $$x < -5 - 10$$ $$x < -15$$ - For $$x+10 > 5$$: $$x > 5 - 10$$ $$x > -5$$ 5. **Combine the solution:** $$x < -15 \quad \text{or} \quad x > -5$$ 6. **Interpretation:** The values of $$x$$ are all numbers less than $$-15$$ or greater than $$-5$$. **Final answer:** $$x < -15 \quad \text{or} \quad x > -5$$