Where did I go wrong in my approach?

Question

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?

Answer 1

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 $(y+1)(y-1) \ge 0$.