1. **State the problem:** Solve the equation $3x - 7 = 9x + 8$ for $x$. 2. **Write down the equation:** $$3x - 7 = 9x + 8$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Subtract $3x$ from both sides to get all $x$ terms on the right:** $$3x - 7 - 3x = 9x + 8 - 3x$$ $$-7 = 6x + 8$$ 5. **Subtract 8 from both sides to isolate the $x$ term:** $$-7 - 8 = 6x + 8 - 8$$ $$-15 = 6x$$ 6. **Divide both sides by 6 to solve for $x$:** $$x = \frac{-15}{6}$$ 7. **Simplify the fraction:** $$x = \frac{-15}{6} = \frac{-5}{2}$$ **Final answer:** $$x = -\frac{5}{2}$$