## Answer :

**Answer:**

x = 3

**Step-by-step explanation:**

Given **mean group data**:

- [tex]8,11,8,10,6,7,3x,11,11[/tex]

To find the value of x we simply add the total ages by combining like terms divided by the sum of data set which gives us 9 years.

[tex]\dotfill[/tex]

[tex]\\\boxed{\begin{array}{l}\underline{\textsf{Mean Group}}\\\\\sf \frac{8+11+8+10+6+7+3x+11+11}{9}=9\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$8+11+8+10+6+7+3x+11+11$ is the dataset.}\\\phantom{ww}\bullet\;\textsf{9 - (Denominator) is the number of dataset.}\\\phantom{ww}\bullet\;\textsf{9 - (RHS) is the known average of the dataset with the unknown(x)}\end{array}}[/tex]

__Steps:__

- Cross-multiply the equation

[tex]\frac{8+11+8+10+6+7+3x+11+11}{9}=9[/tex]

[tex]8+11+8+10+6+7+3x+11+11=9 \times 9[/tex] - Comine like terms

[tex]8+11+8+10+6+7+3x+11+11=81[/tex]

[tex](8+11+8+10+6+7+11+11)+3x=81[/tex] - Add values

[tex]3x + 72 = 81[/tex] - Substract 72 from both sides

[tex]3x = 81 - 72[/tex]

[tex]3x = 9[/tex]

[tex]x = \frac{9}{3}[/tex]

[tex]x=3[/tex]

Therefore, the **value of x simplifies** to:

[tex]\boxed{ \boxed{x=3}}[/tex]