Question

Why is it necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number. Provide an example to support your explanation.

Answer 1

if we start out with
-1 < 2
if we multiply both sides by -1 the numbers become
1 and -2
so to make the inequality work, you have to switch it
1>-2

Answer 2

exactly - when you multiply by a -1, you change the value of each side (making them either higher or lower value - opposite) of what they were before.

Answer 3

for example:
2<5 -- we know that 2 is less than 5 {-1,0,2,3,4,5,6,7,8}
multiply by -1
-2>-5 --- obviously -2 is more that -5 {-7,-6,-5,-4,-3,-2,-1,0,1,....}