1. **State the problem:** Solve the equation $5 - 4(x - 3) = x - 2(x - 1)$ for $x$. 2. **Apply the distributive property:** $$5 - 4x + 12 = x - 2x + 2$$ 3. **Simplify both sides:** $$17 - 4x = -x + 2$$ 4. **Bring all $x$ terms to one side and constants to the other:** $$17 - 4x + x = 2$$ $$17 - 3x = 2$$ 5. **Isolate the $x$ term:** $$-3x = 2 - 17$$ $$-3x = -15$$ 6. **Divide both sides by $-3$ to solve for $x$:** $$x = \frac{-15}{-3}$$ $$x = \cancel{-15} \div \cancel{-3} = 5$$ 7. **Final answer:** $$\boxed{5}$$