1. **State the problem:** Solve the inequality $\left|\frac{1}{2}w - \frac{3}{4}\right| < 2$. 2. **Recall the rule for absolute value inequalities:** If $|A| < b$, then $-b < A < b$. 3. **Apply the rule:** \[-2 < \frac{1}{2}w - \frac{3}{4} < 2\] 4. **Add $\frac{3}{4}$ to all parts to isolate the term with $w$:** \[-2 + \frac{3}{4} < \frac{1}{2}w < 2 + \frac{3}{4}\] Convert $-2$ and $2$ to quarters: \[-\frac{8}{4} + \frac{3}{4} < \frac{1}{2}w < \frac{8}{4} + \frac{3}{4}\] Simplify: \[-\frac{5}{4} < \frac{1}{2}w < \frac{11}{4}\] 5. **Multiply all parts by 2 to solve for $w$:** $$2 \times \left(-\frac{5}{4}\right) < 2 \times \frac{1}{2}w < 2 \times \frac{11}{4}$$ Intermediate step showing cancellation: $$\cancel{2} \times \left(-\frac{5}{4}\right) < \cancel{2} \times \frac{1}{2}w < \cancel{2} \times \frac{11}{4}$$ Simplify: $$-\frac{10}{4} < w < \frac{22}{4}$$ Simplify fractions: $$-\frac{5}{2} < w < \frac{11}{2}$$ 6. **Final answer:** \[-\frac{5}{2} < w < \frac{11}{2}\] 7. **Interval notation:** $\left(-\frac{5}{2}, \frac{11}{2}\right)$ 8. **Decimal form:** $-2.5 < w < 5.5$