Respuesta :
[tex]21k - 3n + 9p > 3p + 12 \\ 3n < 21k + 9p - 3p - 12 \\ n < 7k + 3p - p - 4[/tex]
[tex]n < 2p + 7k - 4[/tex]
Answer: The correct option is
(D) [tex]n<2p+7k-4.[/tex]
Step-by-step explanation: We are given to solve the following inequality for the unknown variable n :
[tex]21k-3n+9p>3p+12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given inequality for n, we must take terms involving n on the left side and other terms on the right side of the inequality.
From inequality (i), we have
[tex]21k-3n+9p>3p+12\\\\\Rightarrow -3n>3p+12-21k-9p\\\\\Rightarrow -3n>-6p-21k+12\\\\\Rightarrow 3n<6p+21k-12~~~~~~~~~~~~~~~~~[\textup{since }a>b~~\Rightarrow -a<-b]\\\\\Rightarrow n<\dfrac{6p+21k-12}{3}\\\\\Rightarrow n<2p+7k-4.[/tex]
Thus, the required solution for n is [tex]n<2p+7k-4.[/tex]
Option (D) is CORRECT.
