Let the two consecutive odd numbers be $x$ (the lesser number) and $x + 2$ (the greater number).

According to the problem:

• Three times the lesser number is $3x$.
• Two times the greater number is $2(x + 2)$.
• We are told that three times the lesser number is eleven more than two times the greater number, so the equation is:

$3x = 2(x + 2) + 11$

Step 1: Expand and simplify the equation

First, expand the right-hand side:

$3x = 2x + 4 + 11$ $3x = 2x + 15$

Step 2: Solve for $x$

Subtract $2x$ from both sides:

$x = 15$

Step 3: Find the two numbers

The lesser number is $x = 15$, and the greater number is $x + 2 = 17$.

Final Answer:

The two consecutive odd numbers are $15$ and $17$.

Would you like more details or have any questions?

---

Here are five related questions:

1. What would the equation be if the numbers were consecutive even numbers?
2. How can we check the solution to ensure it's correct?
3. What happens if we change the condition to "four times the lesser number"?
4. Can you solve for consecutive even numbers under a similar condition?
5. How would the equation change if the numbers were two apart but not necessarily odd?

Tip: When dealing with consecutive integers, use variables like $x$ for the first and $x + 2$, $x + 4$, etc., for the others.