`2x - 13 , 2x - 11, 2x-9, 2x-7` are consecutive_______ Numbers.
where x is a natural number

Options

A. even numbers
B. odd numbers
C. natural numbers
D. prime numbers

Answer

To determine what type of numbers the expressions \(2x - 13\), \(2x - 11\), \(2x - 9\), and \(2x - 7\) represent, we can follow these steps:

### Step 1: Identify the expressions
We have the following expressions:
- \(a = 2x - 13\)
- \(b = 2x - 11\)
- \(c = 2x - 9\)
- \(d = 2x - 7\)

### Step 2: Substitute a natural number for \(x\)
Let’s substitute \(x = 10\) (a natural number) into the expressions to see what numbers we get:
- \(a = 2(10) - 13 = 20 - 13 = 7\)
- \(b = 2(10) - 11 = 20 - 11 = 9\)
- \(c = 2(10) - 9 = 20 - 9 = 11\)
- \(d = 2(10) - 7 = 20 - 7 = 13\)

### Step 3: List the resulting numbers
The resulting numbers are:
- \(7\)
- \(9\)
- \(11\)
- \(13\)

### Step 4: Check if the numbers are consecutive
Now we check if these numbers are consecutive:
- The sequence \(7, 9, 11, 13\) is indeed consecutive.

### Step 5: Determine the type of numbers
Next, we check the type of these numbers:
- **Odd Numbers**: All of these numbers (7, 9, 11, 13) are odd.
- **Natural Numbers**: All of these numbers are also natural numbers.
- **Even Numbers**: None of these numbers are even.
- **Prime Numbers**: 7, 11, and 13 are prime, but 9 is not.

### Conclusion
Since the numbers are consecutive and all are odd, we conclude that \(2x - 13\), \(2x - 11\), \(2x - 9\), and \(2x - 7\) are consecutive odd numbers.

### Final Answer
The expressions \(2x - 13\), \(2x - 11\), \(2x - 9\), and \(2x - 7\) are consecutive **odd numbers**.

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