1. **State the problem:** Solve the equation $$\frac{2x + 1}{3} = -3$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side. Since $2x + 1$ is divided by 3, multiply both sides by 3 to cancel the denominator. 3. **Multiply both sides by 3:** $$\cancel{3} \times \frac{2x + 1}{\cancel{3}} = -3 \times 3$$ which simplifies to $$2x + 1 = -9$$ 4. **Isolate $2x$ by subtracting 1 from both sides:** $$2x + 1 - 1 = -9 - 1$$ $$2x = -10$$ 5. **Solve for $x$ by dividing both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{-10}{\cancel{2}}$$ $$x = -5$$ **Final answer:** $$x = -5$$