1. **State the problem:** Solve for $x$ in the equation $5x - 7 = 3x + 9$. 2. **Write down the equation:** $$5x - 7 = 3x + 9$$ 3. **Isolate the variable terms on one side:** Subtract $3x$ from both sides: $$5x - 3x - 7 = 9$$ Simplify: $$2x - 7 = 9$$ 4. **Isolate the constant term:** Add $7$ to both sides: $$2x = 9 + 7$$ $$2x = 16$$ 5. **Solve for $x$:** Divide both sides by $2$: $$x = \frac{16}{2}$$ $$x = 8$$ **Final answer:** $$x = 8$$