The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x

Sure, let's solve this step by step:

1. First, let's understand the problem. We know that the mean (average) of the numbers 6, 8, x + 2, 10, 2x - 1, and 2 is 9. The mean is calculated by adding all the numbers together and dividing by the number of numbers.

2. So, we can set up the equation: (6 + 8 + x + 2 + 10 + 2x - 1 + 2) / 6 = 9

3. Simplify the equation: (27 + 3x) / 6 = 9

4. Multiply both sides by 6 to get rid of the denominator on the left side: 27 + 3x = 54

5. Subtract 27 from both sides: 3x = 27

6. Divide both sides by 3 to solve for x: x = 9

So, the value of x that makes the mean of the numbers 9 is x = 9.