1. **State the problem:** Solve the linear equation $2x + 5 = 0$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 5 from both sides, then divide both sides by 2. 3. **Step 1: Subtract 5 from both sides** $$2x + 5 - 5 = 0 - 5$$ $$2x = -5$$ 4. **Step 2: Divide both sides by 2** $$\frac{\cancel{2}x}{\cancel{2}} = \frac{-5}{2}$$ $$x = -\frac{5}{2}$$ 5. **Final answer:** $$x = -\frac{5}{2}$$ This means the value of $x$ that satisfies the equation is $-2.5$.