1. **State the problem:** Solve the equation $2x - 5 = 3x + 7$ for $x$. 2. **Write down the equation:** $$2x - 5 = 3x + 7$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Subtract $2x$ from both sides:** $$\cancel{2x} - 5 = 3x - \cancel{2x} + 7 \implies -5 = x + 7$$ 5. **Subtract 7 from both sides:** $$-5 - 7 = x + \cancel{7} - \cancel{7} \implies -12 = x$$ 6. **Final answer:** $$x = -12$$ This means the value of $x$ that satisfies the equation is $-12$.