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