Find the mean of `x+3,x+5,x+7,x+9` and `x+11`.

Answer

To find the mean of the numbers \( x+3, x+5, x+7, x+9, \) and \( x+11 \), we can follow these steps:

### Step-by-Step Solution:

1. **List the Observations**:
The given observations are:
\[ x + 3, \quad x + 5, \quad x + 7, \quad x + 9, \quad x + 11 \]

2. **Calculate the Sum of Observations**:
We need to add all the observations together:
\[ (x + 3) + (x + 5) + (x + 7) + (x + 9) + (x + 11) \]
Combine like terms:
\[ = x + x + x + x + x + (3 + 5 + 7 + 9 + 11) \]
This simplifies to:
\[ = 5x + (3 + 5 + 7 + 9 + 11) \]
Now, calculate the sum of the constants:
\[ 3 + 5 = 8, \quad 8 + 7 = 15, \quad 15 + 9 = 24, \quad 24 + 11 = 35 \]
So, the total sum is:
\[ 5x + 35 \]

3. **Count the Total Number of Observations**:
There are 5 observations in total.

4. **Calculate the Mean**:
The mean is calculated by dividing the sum of the observations by the total number of observations:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Total Number of Observations}} = \frac{5x + 35}{5} \]

5. **Simplify the Mean**:
We can simplify the expression:
\[ = \frac{5x}{5} + \frac{35}{5} = x + 7 \]

### Final Answer:
The mean of the given observations is:
\[ \boxed{x + 7} \]