Question

Solve for n: 21k − 3n + 9p > 3p + 12. (2 points) n > −4p − 7k + 4

n > 2p + 7k − 4 n < −4p − 7k + 4 n < 2p + 7k − 4

Answer 1

`21k - 3n + 9p > 3p + 12 \\ 3n < 21k + 9p - 3p - 12 \\ n < 7k + 3p - p - 4`

`n < 2p + 7k - 4`

Answer 2

Answer: The correct option is

(D)
`n<2p+7k-4.`

Step-by-step explanation: We are given to solve the following inequality for the unknown variable n :

`21k-3n+9p>3p+12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

`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<(6p+21k-12)/(3)\\\\\Rightarrow n<2p+7k-4.`

Thus, the required solution for n is
`n<2p+7k-4.`

Option (D) is CORRECT.