1. **State the problem:** Solve for $x$ in the equation $4x + 1 - 2x + 2 = 0$. 2. **Combine like terms:** Group the $x$ terms and the constants. $$4x - 2x + 1 + 2 = 0$$ 3. Simplify the expression: $$2x + 3 = 0$$ 4. **Isolate $x$:** Subtract 3 from both sides. $$2x + \cancel{3} - \cancel{3} = 0 - 3$$ $$2x = -3$$ 5. **Solve for $x$:** Divide both sides by 2. $$\frac{2x}{\cancel{2}} = \frac{-3}{\cancel{2}}$$ $$x = -\frac{3}{2}$$ **Final answer:** $$x = -\frac{3}{2}$$