1. **State the problem:** Solve the equation $5x - 3[7 - 4(3 - 2x)] = 5(3 - x) - 4$ for $x$. 2. **Apply the distributive property inside the brackets:** Inside the brackets, calculate $4(3 - 2x) = 12 - 8x$. So the expression becomes: $$5x - 3[7 - (12 - 8x)] = 5(3 - x) - 4$$ 3. **Simplify inside the brackets:** $$7 - (12 - 8x) = 7 - 12 + 8x = -5 + 8x$$ 4. **Rewrite the equation:** $$5x - 3(-5 + 8x) = 5(3 - x) - 4$$ 5. **Distribute $-3$ on the left side:** $$5x + 15 - 24x = 15 - 5x - 4$$ 6. **Simplify both sides:** Left side: $5x - 24x + 15 = -19x + 15$ Right side: $15 - 5x - 4 = 11 - 5x$ 7. **Set the equation:** $$-19x + 15 = 11 - 5x$$ 8. **Bring variables to one side and constants to the other:** Add $19x$ to both sides: $$15 = 11 - 5x + 19x$$ Simplify: $$15 = 11 + 14x$$ Subtract 11 from both sides: $$15 - 11 = 14x$$ $$4 = 14x$$ 9. **Solve for $x$:** $$x = \frac{4}{14} = \frac{2}{7}$$ **Final answer:** $$x = \frac{2}{7}$$