1. **State the problem:** Solve the equation $4x - 8 + 5 = 1 - 3x - 9 + 12x$ for $x$. 2. **Simplify both sides:** Left side: $4x - 8 + 5 = 4x - 3$ Right side: $1 - 3x - 9 + 12x = (1 - 9) + (-3x + 12x) = -8 + 9x$ So the equation becomes: $$4x - 3 = -8 + 9x$$ 3. **Bring all $x$ terms to one side and constants to the other:** Subtract $4x$ from both sides: $$\cancel{4x} - 3 = -8 + 9x - \cancel{4x}$$ which simplifies to: $$-3 = -8 + 5x$$ Add $8$ to both sides: $$-3 + 8 = -8 + 8 + 5x$$ which simplifies to: $$5 = 5x$$ 4. **Solve for $x$ by dividing both sides by 5:** $$\frac{5}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ which simplifies to: $$1 = x$$ 5. **Final answer:** $$x = 1$$