Answer
The direction of the inequality symbol is reversed when you multiply or divide an inequality by a negative number.
Work Step by Step
Take the inequality: $ 5 \lt 20$ as an eample.
When multiplying the inequality by $-1$,
$-5 \lt -20$.
This is false as -5 should be greater than -20.
So this is only true when the inequality sign is reversed.
$-5 \gt -20$
A larger magnitude of a positive value is larger than a smaller magnitude of a positive value. However, a smaller magnitude of a negative value is larger than a larger magnitude of a negative value. Hence, the inequality sign is reversed when multiplying or dividing by a negative value.
See "question 84" as another example.