1. **State the problem:** Solve the equation $1 + 2(4x - 9) = x$ for $x$. 2. **Use the distributive property:** Multiply $2$ by each term inside the parentheses: $$1 + 2 \times 4x - 2 \times 9 = x$$ which simplifies to $$1 + 8x - 18 = x$$ 3. **Combine like terms on the left side:** $$8x + (1 - 18) = x$$ $$8x - 17 = x$$ 4. **Isolate the variable terms:** Subtract $x$ from both sides: $$8x - x - 17 = 0$$ $$7x - 17 = 0$$ 5. **Solve for $x$:** Add $17$ to both sides: $$7x = 17$$ Then divide both sides by $7$: $$x = \frac{17}{7}$$ **Final answer:** $$x = \frac{17}{7}$$