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