$$x^2-6x-7\ge 0$$

Steps I took:

$$(x-7)(x+1)\ge 0$$

$$x-7\ge 0\quad x+1\ge0$$

$$x\ge 7\quad x\ge -1$$

When I test the solution set, I realize that it must be $x\ge 7\quad or\quad x\le -1$

What is going on here?