1. **State the problem:** Solve the compound inequality $$5 < \frac{4x - 16}{8} < 8$$ and find the range for $$x$$. 2. **Recall the rule for compound inequalities:** We can multiply or divide all parts of the inequality by the same positive number without changing the inequality signs. 3. Multiply all parts of the inequality by 8 to eliminate the denominator: $$5 \times 8 < \frac{4x - 16}{8} \times 8 < 8 \times 8$$ $$40 < 4x - 16 < 64$$ 4. Add 16 to all parts to isolate the term with $$x$$: $$40 + 16 < 4x - 16 + 16 < 64 + 16$$ $$56 < 4x < 80$$ 5. Divide all parts by 4 to solve for $$x$$: $$\frac{56}{4} < \frac{4x}{4} < \frac{80}{4}$$ 6. Show cancellation step: $$\frac{\cancel{56}}{\cancel{4}} < x < \frac{\cancel{80}}{\cancel{4}}$$ 7. Simplify: $$14 < x < 20$$ **Final answer:** $$14 < x < 20$$