Inequality Solve 5Dec19

1. **State the problem:** Solve the inequality $$\frac{-2z-3}{3} < 5$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator to eliminate the fraction. Since the denominator 3 is positive, the inequality direction remains the same. 3. **Multiply both sides by 3:** $$\cancel{3} \times \frac{-2z-3}{\cancel{3}} < 5 \times 3$$ $$-2z - 3 < 15$$ 4. **Add 3 to both sides:** $$-2z - 3 + 3 < 15 + 3$$ $$-2z < 18$$ 5. **Divide both sides by -2:** Since we divide by a negative number, the inequality direction reverses. $$\frac{-2z}{-2} > \frac{18}{-2}$$ $$z > -9$$ **Final answer:** $$z > -9$$