1. **State the problem:** We need to find the value of $x$ in the equation $3x + 5 = 0$. 2. **Formula and rules:** To solve for $x$, we isolate $x$ by performing inverse operations. Subtract 5 from both sides, then divide both sides by 3. 3. **Step-by-step solution:** $$3x + 5 = 0$$ Subtract 5 from both sides: $$3x = -5$$ Divide both sides by 3: $$x = \frac{-5}{3}$$ 4. **Explanation:** We moved the constant term to the right side by subtracting 5, then divided by the coefficient of $x$ (which is 3) to isolate $x$. This gives the solution $x = -\frac{5}{3}$. **Final answer:** $$x = -\frac{5}{3}$$