Why does the inequality sign change when both sides are multiplied or divided by a negative number? does this happen with equations? why or why not?

2<3 | * - 2

if the sign it is not changed ⇒ - 4 < - 6 but it is false (the negative number is bigger when the number after is smaller)

⇒the sign must be changed

- 4 > - 6

but in equation the sign remain " = "

⇒ in equation the change does not happen

Ex 3=2+1 | - 2

-3 * (-2) = - 6 = - 2 * (2+1) = - 4 - 2 true