1. **State the problem:** Solve the linear equation $2x + 45 = 12$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 45 from both sides, then divide both sides by 2. 3. **Step-by-step solution:** - Subtract 45 from both sides: $$2x + 45 - 45 = 12 - 45$$ $$2x = -33$$ - Divide both sides by 2: $$x = \frac{-33}{2}$$ 4. **Final answer:** $$x = -\frac{33}{2}$$ or $$x = -16.5$$