Option (D) 3
Mean = $\dfrac{2+9+(x+6)+(2x+3)+5+10+5}{7} = 7$
$\Rightarrow 2+9+x+6+2x+3+5+10+5 = 49$
$\Rightarrow 3x + 40 = 49 \Rightarrow 3x = 9 \Rightarrow x = 3$
Apply the mean formula: sum of all observations ÷ total number of observations = given mean. Set up the equation, simplify by collecting like terms, and solve for x. There are 7 observations, so multiply mean (7) by 7 to get 49. Watch out for correctly expanding $(x+6)$ and $(2x+3)$ before adding.