1. **State the problem:** Solve the equation $3a(2-2x) = -4a + x$ for $x$. 2. **Distribute the left side:** Use the distributive property $a(b+c) = ab + ac$. $$3a(2-2x) = 3a \cdot 2 - 3a \cdot 2x = 6a - 6ax$$ 3. **Rewrite the equation:** $$6a - 6ax = -4a + x$$ 4. **Group terms with $x$ on one side and constants on the other:** Add $6ax$ to both sides and add $4a$ to both sides: $$6a + 4a = x + 6ax$$ $$10a = x + 6ax$$ 5. **Factor $x$ on the right side:** $$10a = x(1 + 6a)$$ 6. **Solve for $x$ by dividing both sides by $(1 + 6a)$:** $$x = \frac{10a}{1 + 6a}$$ **Final answer:** $$x = \frac{10a}{1 + 6a}$$