When you divide both sides of any inequality by a negative number, you need the inequality symbol?

Reverse the inequality symbol.

Explanation:
Two simple examples explain the answer.

Example 1.
 -3 < 2       True
Multiply each side by -1.
Is (-3)*(-1) < (2)*(-1)?
3 < -2       False
3 > - 2      True
The inequality sign is reversed to make the sttement True.

Example 2.
3 > - 2          True
Multiply each side by -1.
3*(-1) > (-2)*(-1) ?
-3 > 2          False
-3 < 2          True
The inequalty sign is reversed to make the statement True.