**Finding the Four Consecutive Odd Numbers**

To find four consecutive odd numbers whose sum is 128, we can use algebraic expressions. Let's assume the first odd number as 'x'. Since we need four consecutive odd numbers, the next three odd numbers can be represented as 'x + 2', 'x + 4', and 'x + 6' respectively.

**Setting up the Equation**

We can now set up the equation to find the sum of these four consecutive odd numbers:

x + (x + 2) + (x + 4) + (x + 6) = 128

**Simplifying the Equation**

To solve the equation, we simplify it by combining like terms:

4x + 12 = 128

Subtracting 12 from both sides:

4x = 116

Dividing both sides by 4:

x = 29

**Finding the Consecutive Odd Numbers**

Now that we have the value of the first odd number (x = 29), we can find the other three consecutive odd numbers:

First odd number: x = 29
Second odd number: x + 2 = 29 + 2 = 31
Third odd number: x + 4 = 29 + 4 = 33
Fourth odd number: x + 6 = 29 + 6 = 35

Therefore, the four consecutive odd numbers whose sum is 128 are 29, 31, 33, and 35.

**Explanation in Detail**

The question asks us to find four consecutive odd numbers whose sum is 128. To solve this problem, we can set up an algebraic equation by assuming the first odd number as 'x'. Since we need four consecutive odd numbers, the next three odd numbers can be represented as 'x + 2', 'x + 4', and 'x + 6' respectively.

By adding up these four consecutive odd numbers and equating the sum to 128, we can set up the equation:

x + (x + 2) + (x + 4) + (x + 6) = 128

Simplifying the equation, we combine like terms:

4x + 12 = 128

To isolate the variable 'x', we subtract 12 from both sides:

4x = 116

Next, we divide both sides of the equation by 4 to solve for 'x':

x = 29

Now that we have the value of the first odd number, we can find the other three consecutive odd numbers by substituting 'x' into the expressions:

First odd number: x = 29
Second odd number: x + 2 = 29 + 2 = 31
Third odd number: x + 4 = 29 + 4 = 33
Fourth odd number: x + 6 = 29 + 6 = 35

Therefore, the four consecutive odd numbers whose sum is 128 are 29, 31, 33, and 35.

Let the first odd number be x
second number be x+2, third number be x+4, fourth number be x+6
so given that,
x+x+2+x+4+x+6=128
again, 4x+12=128
so, 4x=128-12=116
so, x=116/4=29
Therefore, the four numbers are,
x=29, x+2=29+2=31, x+4=29+4=33, x+6=29+6=35