1. **State the problem:** Solve for $x$ in the equation $$-4x + 2(x + 4) = -7x - (x + 1)$$. 2. **Apply the distributive property:** Expand the terms with parentheses. $$-4x + 2x + 8 = -7x - x - 1$$ 3. **Combine like terms on each side:** Left side: $$-4x + 2x = -2x$$ Right side: $$-7x - x = -8x$$ So the equation becomes: $$-2x + 8 = -8x - 1$$ 4. **Isolate variable terms on one side:** Add $8x$ to both sides. $$-2x + 8x + 8 = -8x + 8x - 1$$ $$6x + 8 = -1$$ 5. **Isolate the constant term:** Subtract 8 from both sides. $$6x + \cancel{8} - \cancel{8} = -1 - 8$$ $$6x = -9$$ 6. **Solve for $x$ by dividing both sides by 6:** $$x = \frac{-9}{6}$$ 7. **Simplify the fraction:** $$x = \frac{\cancel{ -9 }}{\cancel{6}} = \frac{-3}{2}$$ **Final answer:** $$x = -\frac{3}{2}$$