1. Let's solve the first inequality: $$\frac{5x + 2}{4} < \frac{18}{5}$$ 2. To eliminate the denominators, multiply both sides by 20 (the least common multiple of 4 and 5): $$20 \times \frac{5x + 2}{4} < 20 \times \frac{18}{5}$$ 3. Simplify both sides: $$\cancel{20} \times \frac{5x + 2}{\cancel{4}} = 5 \times (5x + 2) = 25x + 10$$ $$\cancel{20} \times \frac{18}{\cancel{5}} = 4 \times 18 = 72$$ So the inequality becomes: $$25x + 10 < 72$$ 4. Subtract 10 from both sides: $$25x + 10 - 10 < 72 - 10$$ $$25x < 62$$ 5. Divide both sides by 25: $$\frac{25x}{25} < \frac{62}{25}$$ $$x < \frac{62}{25}$$ 6. The solution set in interval notation is: $$( -\infty, \frac{62}{25} )$$ 7. Now, solve the second inequality: $$5z - 2 > 4z - 8$$ 8. Subtract $4z$ from both sides: $$5z - 4z - 2 > 4z - 4z - 8$$ $$z - 2 > -8$$ 9. Add 2 to both sides: $$z - 2 + 2 > -8 + 2$$ $$z > -6$$ 10. The solution set in interval notation is: $$( -6, \infty )$$ 11. Finally, solve the third inequality: $$-6(3y - 6) < -24y - 6$$ 12. Distribute $-6$ on the left side: $$-18y + 36 < -24y - 6$$ 13. Add $24y$ to both sides: $$-18y + 24y + 36 < -24y + 24y - 6$$ $$6y + 36 < -6$$ 14. Subtract 36 from both sides: $$6y + 36 - 36 < -6 - 36$$ $$6y < -42$$ 15. Divide both sides by 6: $$\frac{6y}{6} < \frac{-42}{6}$$ $$y < -7$$ 16. The solution set in interval notation is: $$( -\infty, -7 )$$