1. **State the problem:** Solve the linear equation $$2(-4x + 2) - 3x - 3 = 8$$ for $x$. 2. **Apply the distributive property:** Multiply 2 by each term inside the parentheses: $$2 \times -4x = -8x$$ $$2 \times 2 = 4$$ So the equation becomes: $$-8x + 4 - 3x - 3 = 8$$ 3. **Combine like terms on the left side:** $$-8x - 3x + 4 - 3 = 8$$ $$-11x + 1 = 8$$ 4. **Isolate the variable term:** Subtract 1 from both sides: $$-11x + 1 - 1 = 8 - 1$$ $$-11x = 7$$ 5. **Solve for $x$ by dividing both sides by $-11$:** $$x = \frac{7}{\cancel{-11}} \times \frac{\cancel{-1}}{1} = -\frac{7}{11}$$ **Final answer:** $$x = -\frac{7}{11}$$