The solution set of the in equation  $x+2\le 8,\forall x\in N$ is

Given inequation is $x+2\le 8,\forall x\in N$

Both sides subtracting by 2

$x+2-2\le 8-2$

$x\le 6(\because N=\{1,2,3,\mathrm{.....}\})$

Since $x\in N$and $x\le 6$then  $x=1, 2, 3, 4, 5, 6$

$\therefore$ The solution set is  $\{1, 2, 3, 4, 5, 6\}$