1. **State the problem:** Solve the equation $$\frac{5 - 3x}{2} = 12$$ for $x$. 2. **Formula and rules:** To solve for $x$, we first eliminate the denominator by multiplying both sides by 2. Then isolate $x$ by performing inverse operations. 3. **Step-by-step solution:** Multiply both sides by 2: $$5 - 3x = 12 \times 2$$ $$5 - 3x = 24$$ Subtract 5 from both sides: $$-3x = 24 - 5$$ $$-3x = 19$$ Divide both sides by $-3$: $$x = \frac{19}{-3}$$ $$x = -\frac{19}{3}$$ 4. **Final answer:** $$x = -\frac{19}{3}$$