1. **State the problem:** Solve the linear equation $$-2(9x - 1) = -(x - 9) - 7x$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses on the left side, and distribute the negative sign on the right side: $$-2 \times 9x + (-2) \times (-1) = -1 \times x + (-1) \times (-9) - 7x$$ which simplifies to $$-18x + 2 = -x + 9 - 7x$$ 3. **Combine like terms on the right side:** $$-18x + 2 = (-x - 7x) + 9$$ $$-18x + 2 = -8x + 9$$ 4. **Isolate variable terms on one side and constants on the other:** Add $18x$ to both sides and subtract $9$ from both sides: $$-18x + 2 + 18x - 9 = -8x + 9 + 18x - 9$$ which simplifies to $$2 - 9 = (-8x + 18x)$$ $$-7 = 10x$$ 5. **Solve for $x$ by dividing both sides by 10:** $$x = \frac{-7}{10}$$ 6. **Final answer:** $$\boxed{x = -\frac{7}{10}}$$