1. **State the problem:** Solve the equation $3a(2-2x) = -4a = x$ for $x$. 2. **Analyze the equation:** The equation as given is ambiguous because it contains two equal signs. We interpret it as two separate equations: - $3a(2-2x) = -4a$ - $-4a = x$ 3. **Solve the first equation:** $$3a(2-2x) = -4a$$ Expand the left side: $$6a - 6ax = -4a$$ 4. **Rearrange terms:** $$6a - 6ax = -4a$$ Move $6a$ to the right: $$-6ax = -4a - 6a$$ $$-6ax = -10a$$ 5. **Divide both sides by $-6a$ (assuming $a \neq 0$):** $$x = \frac{-10a}{-6a} = \frac{10}{6} = \frac{5}{3}$$ 6. **Use the second equation to find $x$:** $$x = -4a$$ 7. **Equate the two expressions for $x$:** $$\frac{5}{3} = -4a$$ 8. **Solve for $a$:** $$a = -\frac{5}{12}$$ 9. **Find $x$ using $x = -4a$:** $$x = -4 \times \left(-\frac{5}{12}\right) = \frac{20}{12} = \frac{5}{3}$$ **Final answer:** $$a = -\frac{5}{12}, \quad x = \frac{5}{3}$$