1. **State the problem:** Solve the equation $3x - 4 = 5x + 2$ for $x$. 2. **Write down the equation:** $$3x - 4 = 5x + 2$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Subtract $3x$ from both sides:** $$\cancel{3x} - 4 = 5x - \cancel{3x} + 2 \implies -4 = 2x + 2$$ 5. **Subtract 2 from both sides:** $$-4 - 2 = 2x + \cancel{2} - \cancel{2} \implies -6 = 2x$$ 6. **Divide both sides by 2 to solve for $x$:** $$\frac{-6}{\cancel{2}} = \frac{2x}{\cancel{2}} \implies -3 = x$$ 7. **Final answer:** $$x = -3$$