1. **State the problem:** Solve the linear equation $2x + 3 = 0$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. 3. **Step-by-step solution:** - Subtract 3 from both sides: $$2x + 3 - 3 = 0 - 3$$ $$2x = -3$$ - Divide both sides by 2 to isolate $x$: $$x = \frac{-3}{2}$$ 4. **Final answer:** $$x = -\frac{3}{2}$$ This means the value of $x$ that satisfies the equation is $-1.5$.