1. **State the problem:** Solve the linear equation $$2x = -1 + 8(2x + 1)$$ for $x$. 2. **Apply the distributive property:** Multiply $8$ by each term inside the parentheses: $$2x = -1 + 8 \times 2x + 8 \times 1$$ $$2x = -1 + 16x + 8$$ 3. **Combine like terms on the right side:** $$2x = 16x + (-1 + 8)$$ $$2x = 16x + 7$$ 4. **Isolate variable terms on one side:** Subtract $16x$ from both sides: $$2x - 16x = 7$$ $$\cancel{2x} - \cancel{16x} = 7$$ $$-14x = 7$$ 5. **Solve for $x$ by dividing both sides by $-14$:** $$x = \frac{7}{-14}$$ $$x = -\frac{1}{2}$$ 6. **Final answer:** $$x = -0.5$$ Note: The provided solution $x = -1.5$ is incorrect based on the steps above.