1. **State the problem:** Solve the equation $1 - \frac{3x}{2} = \frac{5}{4}$ for $x$. 2. **Isolate the term with $x$:** Subtract 1 from both sides: $$1 - \frac{3x}{2} - 1 = \frac{5}{4} - 1$$ which simplifies to $$- \frac{3x}{2} = \frac{5}{4} - \frac{4}{4} = \frac{1}{4}$$ 3. **Solve for $x$:** Multiply both sides by $-\frac{2}{3}$ to isolate $x$: $$x = \cancel{-\frac{2}{3}} \times \cancel{- \frac{3x}{2}} = \cancel{-\frac{2}{3}} \times \frac{1}{4}$$ 4. **Simplify the multiplication:** $$x = -\frac{2}{3} \times \frac{1}{4} = -\frac{2}{12} = -\frac{1}{6}$$ 5. **Final answer:** $$x = -\frac{1}{6}$$