**Problem Statement**

The mean of a data set is the average value of all the observations in the data set. In this problem, we are given a data set consisting of 6 numbers: 6, 8, x, 2, 10, and 2x - 1. We are also given that the mean of this data set is 9. Our task is to find the value of x and the value of the observation in the data set.

**Solution**

To find the value of x and the observation in the data set, we need to use the given information that the mean of the data set is 9. We can start by calculating the sum of all the numbers in the data set and setting it equal to the product of the mean and the number of observations.

Let's break down the solution into steps:

1. **Identify the given numbers:** The given numbers in the data set are 6, 8, x, 2, 10, and 2x - 1.

2. **Write the equation for the mean:** The mean of the data set is given as 9. We can represent the sum of all the numbers in the data set as follows:
(6 + 8 + x + 2 + 10 + 2x - 1)

3. **Set up the equation:** We know that the mean is equal to the sum of the numbers divided by the total number of observations. In this case, the total number of observations is 6. Therefore, we can set up the equation as follows:
(6 + 8 + x + 2 + 10 + 2x - 1) / 6 = 9

4. **Simplify the equation:** To solve the equation, we need to simplify it. First, let's combine like terms in the numerator:
(26 + 3x) / 6 = 9

5. **Multiply both sides by 6:** To eliminate the denominator, we can multiply both sides of the equation by 6:
26 + 3x = 54

6. **Solve for x:** Now, we can solve the equation for x. First, let's isolate the term with x:
3x = 54 - 26
3x = 28

Then, divide both sides by 3 to solve for x:
x = 28 / 3
x = 9.33 (rounded to two decimal places)

7. **Calculate the observation:** Now that we have found the value of x, we can substitute it back into the equation to find the observation in the data set. Let's replace x with 9.33:
Observation = 2x - 1
= 2(9.33) - 1
= 18.66 - 1
= 17.66 (rounded to two decimal places)

**Conclusion**

The value of x in the data set is 9.33, and the observation in the data set is 17.66. We found these values by setting up an equation using the given information that the mean of the data set is 9 and solving for x. By substituting the value of x back into the equation, we were able to find the observation in the data set.

X=6......?