1. **State the problem:** Jessie has 15 3/4 cups of flour and needs to save 2 cups for a cake. Each batch of bread requires 5 1/2 cups of flour. We want to find how many batches $b$ Jessie can make, given these constraints. 2. **Write the inequality:** Jessie must save 2 cups, so the flour available for bread is $15 \frac{3}{4} - 2$ cups. The amount of flour used for $b$ batches is $5 \frac{1}{2} b$ cups. The inequality is: $$5 \frac{1}{2} b \leq 15 \frac{3}{4} - 2$$ 3. **Convert mixed numbers to improper fractions:** $$15 \frac{3}{4} = \frac{63}{4}, \quad 5 \frac{1}{2} = \frac{11}{2}$$ 4. **Simplify the right side:** $$\frac{63}{4} - 2 = \frac{63}{4} - \frac{8}{4} = \frac{55}{4}$$ 5. **Rewrite the inequality:** $$\frac{11}{2} b \leq \frac{55}{4}$$ 6. **Solve for $b$ by multiplying both sides by the reciprocal of $\frac{11}{2}$, which is $\frac{2}{11}$:** $$b \leq \frac{55}{4} \times \frac{2}{11} = \frac{55 \times 2}{4 \times 11} = \frac{110}{44} = \frac{5}{2} = 2.5$$ 7. **Interpretation:** Jessie can make at most 2.5 batches, but since batches must be whole, she can make 2 full batches. **Final answer:** $$b \leq 2.5 \implies \text{maximum full batches} = 2$$