1. **State the problem:** Solve the equation $$2X - 5 = 9X + 2$$ for $X$. 2. **Write down the equation:** $$2X - 5 = 9X + 2$$ 3. **Isolate the variable terms on one side:** Subtract $2X$ from both sides: $$2X - 5 - 2X = 9X + 2 - 2X$$ which simplifies to $$-5 = 7X + 2$$ 4. **Isolate the constant terms on the other side:** Subtract $2$ from both sides: $$-5 - 2 = 7X + 2 - 2$$ which simplifies to $$-7 = 7X$$ 5. **Solve for $X$:** Divide both sides by $7$: $$X = \frac{-7}{7} = -1$$ 6. **Final answer:** The solution to the equation is $$X = -1$$.