Question

Find the integer values of n that satisfies the given inequality
$18-2n<6n\le 30+n$

Answer 1

$18-2n<6n\le 30+n$

$\Rightarrow 18-2n<6n$ and $6n\le 30+n$

$\Rightarrow 18<8n$ and $5n\le 30$

$\Rightarrow \frac{18}{8}<n$ and $n\le \frac{30}{5}$

$\Rightarrow \frac{9}{4}<n$ and $n\le 6$

$\Rightarrow \frac{9}{4}<n\le 6$

Hence possibilities of n are $3,4,5,6.$