1. **Problem statement:** Given the inequality $16 > |12 - 4x|$, find the solution set. 2. **Recall the definition of absolute value inequality:** For $a > |b|$, this means $-a < b < a$. 3. **Apply this to the inequality:** $$16 > |12 - 4x| \implies -16 < 12 - 4x < 16$$ 4. **Solve the compound inequality:** - From $-16 < 12 - 4x$: $$-16 - 12 < -4x \implies -28 < -4x \implies 7 > x$$ - From $12 - 4x < 16$: $$-4x < 4 \implies x > -1$$ 5. **Combine the two inequalities:** $$-1 < x < 7$$ 6. **Final solution set:** $$(-1, 7)$$ **Note:** The options given do not match this solution exactly, so the correct answer is the interval $(-1,7)$.