Answer: The correct option is
(D) 8 and 9.
Step-by-step explanation: We are given to select the correct values of x for which the following inequality is true :
[tex]3(1+x)>x+17~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To select the correct values of x, we must solve the given inequality.
From inequality (i), we have
[tex]3(1+x)>x+17\\\\\Rightarrow 3+3x>x+17\\\\\Rightarrow 3x-x>17-3\\\\\Rightarrow 2x>14\\\\\Rightarrow x>\dfrac{14}{2}\\\\\Rightarrow x>7.[/tex]
Since the value of x is strictly greater than 7, so the correct vaues will be 8 and 9.
Option (D) is CORRECT.
