Dividing by a Negative

The sign flips whenever the coefficient of $x$ is negative. In $-x \ge 4$, the coefficient is -1. Divide both sides by -1 and flip the sign:

$$x \le -4$$

To solve $-5x > -20$, divide both sides by -5 and flip the sign. On the right, -20 divided by -5 is 4, because a negative divided by a negative is positive:

$$x < 4$$

Reverse the sign whenever you divide both sides by a negative number. It does not matter whether the number on the other side is positive or negative. Dividing by -5 reverses the sign in both $-5x > 20$ and $-5x > -20$.