Why the inequality symbol must be reversed when both sides of an inequality are multiplied or divided by a negative number?

Answer 1

The inequality symbol shows wich side of the equation is greater than the other. When you multiply a positive number by a negative number you get a negative result ( for instance 4 x -2 = -8 ). 4 is larger than -8. If we multiply a negative number by a negative number we get a positive number.

1) -5 > -6

. -1 (-5) < -1(-6)

. 5 < 6 this is a true statement

2) 5 > -6

. -1 (5) < -1 (-6)

. -5 < 6 this is also true

3) 6 > 5

. -1 (6) < -1 (5)

. -6 < - 5 this one works too