1. **State the problem:** Solve the equation $3(1 - x) - 2(3 - x) = 4(1 - 2x)$. 2. **Write the formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to expand each term. Then combine like terms and isolate $x$. 3. **Expand each term:** $$3(1 - x) = 3 - 3x$$ $$-2(3 - x) = -6 + 2x$$ $$4(1 - 2x) = 4 - 8x$$ 4. **Rewrite the equation with expanded terms:** $$3 - 3x - 6 + 2x = 4 - 8x$$ 5. **Combine like terms on the left side:** $$3 - 6 = -3$$ $$-3x + 2x = -x$$ So the equation becomes: $$-3 - x = 4 - 8x$$ 6. **Add $x$ to both sides to move $x$ terms to the right:** $$-3 - \cancel{x} = 4 - 8x + \cancel{x}$$ $$-3 = 4 - 7x$$ 7. **Subtract 4 from both sides to isolate terms with $x$ on the right:** $$-3 - 4 = 4 - 4 - 7x$$ $$-7 = -7x$$ 8. **Divide both sides by $-7$ to solve for $x$:** $$\frac{-7}{\cancel{-7}} = \frac{-7x}{\cancel{-7}}$$ $$1 = x$$ 9. **Final answer:** $$\boxed{x = 1}$$