Where did I go wrong in my approach? Consider the two inequalities: $y \le-1$ or $  y\ge 2$  
My approach:
$y \le-1$ or $  y\ge 2$
iff $y+1\le0$ or $y-2 \ge 0$
iff $(y+1)(y-2)\le0$
On solving: $(y+1)(y-2)\le0$
I got $-1\le y\le2$
Where did I do wrong? 

The mistake has been pointed out in the comment.
Now the fix.
Case $1$: If $y+1 \le 0$ , then $y-2\le 0$, hence $(y+1)(y-1) \ge 0$.
Case $2$: if $y-2 \ge 0$, then $y+1 \ge 0$, hence $(y+1)(y-1) \ge 0$.
