1. **State the problem:** Solve the equation $5 - \frac{3x}{2} = 12$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides: $$5 - \frac{3x}{2} - 5 = 12 - 5$$ which simplifies to $$- \frac{3x}{2} = 7$$ 3. **Eliminate the fraction:** Multiply both sides by $-\frac{2}{3}$ to solve for $x$: $$x = 7 \times \left(-\frac{2}{3}\right)$$ 4. **Calculate the product:** $$x = -\frac{14}{3}$$ 5. **Final answer:** $$x = -\frac{14}{3}$$ This means the solution to the equation is $x = -\frac{14}{3}$, or approximately $-4.67$.