1. **State the problem:** Solve for $x$ in the equation $3x - 7 = 2x + 5$. 2. **Write down the equation:** $$3x - 7 = 2x + 5$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$3x - 7 - 2x = 2x + 5 - 2x$$ which simplifies to $$3x - \cancel{2x} - 7 = \cancel{2x} + 5$$ $$x - 7 = 5$$ 4. **Isolate $x$ by adding 7 to both sides:** $$x - 7 + 7 = 5 + 7$$ $$x = 12$$ 5. **Final answer:** $$\boxed{12}$$