1. Solve the inequality $-3a - 1 \frac{1}{2} < -5 \frac{1}{4}$. 2. Solve the inequality $\frac{m}{8} - 2 \frac{1}{2} > -4$. 3. Solve the inequality $\frac{h}{2} + \frac{h}{3} - \frac{1}{2} \leq 5 \frac{1}{3}$. --- ### Step 1: Solve $-3a - 1 \frac{1}{2} < -5 \frac{1}{4}$ 1. Convert mixed numbers to improper fractions: $-3a - \frac{3}{2} < -\frac{21}{4}$ 2. Add $\frac{3}{2}$ to both sides: $$-3a - \frac{3}{2} + \frac{3}{2} < -\frac{21}{4} + \frac{3}{2}$$ $$-3a < -\frac{21}{4} + \frac{6}{4}$$ $$-3a < -\frac{15}{4}$$ 3. Divide both sides by $-3$, remembering to reverse the inequality sign because dividing by a negative number flips the inequality: $$\frac{\cancel{-3}a}{\cancel{-3}} > \frac{ -\frac{15}{4} }{ -3 }$$ $$a > \frac{15}{12} = \frac{5}{4}$$ --- ### Step 2: Solve $\frac{m}{8} - 2 \frac{1}{2} > -4$ 1. Convert mixed number to improper fraction: $$\frac{m}{8} - \frac{5}{2} > -4$$ 2. Add $\frac{5}{2}$ to both sides: $$\frac{m}{8} > -4 + \frac{5}{2}$$ Convert $-4$ to $-\frac{8}{2}$: $$\frac{m}{8} > -\frac{8}{2} + \frac{5}{2} = -\frac{3}{2}$$ 3. Multiply both sides by 8: $$m > 8 \times -\frac{3}{2}$$ $$m > -12$$ --- ### Step 3: Solve $\frac{h}{2} + \frac{h}{3} - \frac{1}{2} \leq 5 \frac{1}{3}$ 1. Convert mixed number to improper fraction: $$\frac{h}{2} + \frac{h}{3} - \frac{1}{2} \leq \frac{16}{3}$$ 2. Add $\frac{1}{2}$ to both sides: $$\frac{h}{2} + \frac{h}{3} \leq \frac{16}{3} + \frac{1}{2}$$ Find common denominator 6: $$\frac{16}{3} = \frac{32}{6}, \quad \frac{1}{2} = \frac{3}{6}$$ So: $$\frac{h}{2} + \frac{h}{3} \leq \frac{32}{6} + \frac{3}{6} = \frac{35}{6}$$ 3. Find common denominator for $\frac{h}{2} + \frac{h}{3}$: $$\frac{3h}{6} + \frac{2h}{6} = \frac{5h}{6}$$ So: $$\frac{5h}{6} \leq \frac{35}{6}$$ 4. Multiply both sides by 6: $$5h \leq 35$$ 5. Divide both sides by 5: $$h \leq 7$$ --- ### Final answers: 1. $a > \frac{5}{4}$ 2. $m > -12$ 3. $h \leq 7$