1. **State the problem:** Simplify the expression $\frac{3}{2}x - x$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients and keep the variable the same. 3. **Rewrite the expression:** $\frac{3}{2}x - 1x$ (since $x = 1x$). 4. **Subtract the coefficients:** $$\frac{3}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{3 - 2}{2} = \frac{1}{2}$$ 5. **Write the simplified expression:** $$\frac{1}{2}x$$ **Final answer:** $\frac{1}{2}x$