You flip the inequality sign when you are dividing or multiplying both sides by a negative.

You also flip the inequality sign when you "swap" the answers on both sides.

The other time you flip the inequality sign is when raising both sides to a negative power. e.g. 5>4, but (5^-1)<(4^-1) i.e. 1/5 < 1/4....this is true when both sides of the inequality are either positive or negative, if one side is positive and one side is negative, the inequality sign does not get flipped, e.g. -4<5 and -1/4 < 1/5 (in this case the inequality sign is not flipped)