1. **State the problem:** Solve the equation $5x + 4 = 0$ for $x$. 2. **Formula and rules:** To solve a linear equation of the form $ax + b = 0$, isolate $x$ by subtracting $b$ from both sides and then dividing by $a$. 3. **Isolate $x$:** $$5x + 4 = 0$$ Subtract 4 from both sides: $$5x = -4$$ 4. **Divide both sides by 5:** $$x = \frac{-4}{5}$$ 5. **Final answer:** $$x = -\frac{4}{5}$$ This means the value of $x$ that satisfies the equation is $-\frac{4}{5}$.