1. **State the problem:** Solve the equation $5x - 4(1 - 3x) = 4x - (x + 1)$ for $x$. 2. **Apply the distributive property:** $$5x - 4 + 12x = 4x - x - 1$$ 3. **Combine like terms on each side:** $$17x - 4 = 3x - 1$$ 4. **Isolate variable terms on one side and constants on the other:** $$17x - 3x = -1 + 4$$ 5. **Simplify both sides:** $$14x = 3$$ 6. **Solve for $x$ by dividing both sides by 14:** $$x = \frac{3}{14}$$ **Final answer:** $x = \frac{3}{14}$