1. **State the problem:** Solve the equation $$-2(x + 2) - x - 3 = 8$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses. $$-2(x + 2) = -2 \times x + (-2) \times 2 = -2x - 4$$ So the equation becomes: $$-2x - 4 - x - 3 = 8$$ 3. **Combine like terms on the left side:** $$-2x - x - 4 - 3 = 8$$ $$-3x - 7 = 8$$ 4. **Isolate the variable term:** Add 7 to both sides. $$-3x - 7 + 7 = 8 + 7$$ $$-3x = 15$$ 5. **Solve for $x$ by dividing both sides by $-3$:** $$x = \frac{15}{\cancel{-3}} \times \frac{\cancel{-1}}{1} = -5$$ 6. **Final answer:** $$x = -5$$