Find all pairs of consecutive odd integers both of which are smaller than 12 and their sum is more than 11.

Explanation

To solve the problem of finding all pairs of consecutive odd integers that are both smaller than 12 and whose sum is more than 11, we can follow these steps:

### Step 1: Define the Consecutive Odd Integers
Let the first consecutive odd integer be \( x \). The next consecutive odd integer can be expressed as \( x + 2 \).

### Step 2: Set Up the Inequalities
We need to satisfy two conditions:
1. Both integers must be smaller than 12.
2. Their sum must be greater than 11.

From the first condition, we have:
- \( x < 12 \)
- \( x + 2 < 12 \)

From the second condition, we have:
- \( x + (x + 2) > 11 \)

### Step 3: Solve the Inequalities
1. From \( x < 12 \), we directly have \( x < 12 \).
2. From \( x + 2 < 12 \):
\[ x < 12 - 2 \implies x < 10 \]
3. From the sum condition \( x + (x + 2) > 11 \):
\[ 2x + 2 > 11 \]
Subtracting 2 from both sides:
\[ 2x > 9 \]
Dividing by 2:
\[ x > 4.5 \]

### Step 4: Combine the Inequalities
Now we combine the inequalities:
- \( 4.5 < x < 10 \)

Since \( x \) must be an odd integer, the possible values for \( x \) are 5, 7, and 9.

### Step 5: Find the Consecutive Odd Integer Pairs
Now we can find the pairs of consecutive odd integers:
- If \( x = 5 \), then the pair is \( (5, 7) \).
- If \( x = 7 \), then the pair is \( (7, 9) \).
- If \( x = 9 \), then the pair is \( (9, 11) \), but 11 is not less than 12.

Thus, the valid pairs of consecutive odd integers that satisfy both conditions are:
- \( (5, 7) \)
- \( (7, 9) \)

### Final Answer
The pairs of consecutive odd integers both smaller than 12 and whose sum is more than 11 are:
- \( (5, 7) \)
- \( (7, 9) \)