1. **State the problem:** Find the largest two consecutive odd integers such that four times the larger reduced by the smaller is less than 100. 2. **Define variables:** Let the smaller odd integer be $x$. Since the integers are consecutive odd integers, the larger one is $x+2$. 3. **Write the inequality:** Four times the larger reduced by the smaller means $4(x+2) - x < 100$. 4. **Simplify the inequality:** $$4(x+2) - x < 100$$ $$4x + 8 - x < 100$$ $$3x + 8 < 100$$ 5. **Isolate $x$:** $$3x < 100 - 8$$ $$3x < 92$$ 6. **Divide both sides by 3:** $$\frac{\cancel{3}x}{\cancel{3}} < \frac{92}{3}$$ $$x < \frac{92}{3} \approx 30.67$$ 7. **Interpret the result:** Since $x$ is an odd integer less than 30.67, the largest odd integer satisfying this is 29. 8. **Find the two integers:** The smaller odd integer is 29, the larger is $29 + 2 = 31$. 9. **Check the inequality:** $$4(31) - 29 = 124 - 29 = 95 < 100$$ which is true. **Final answer:** The largest two consecutive odd integers are **29 and 31**.