Yes, when you multiply or divide both sides of an inequality by a negative number, the inequality sign must be reversed.
Let's solve the inequality -2x - 5 > 19:
First, let's isolate the variable by adding 5 to both sides:
-2x - 5 + 5 > 19 + 5
-2x > 24
Next, divide both sides of the inequality by -2, remembering to reverse the inequality sign:
(-2x)/(-2) < 24/(-2)
x < -12
The solution to the inequality is x < -12.