True or false: If a,b, and c are real numbers, and a<=b, then ac<=bc. Explain and give example

Question

The a<=b is a is less then or equal to b. ac<=bc is ac less then or equal to bc. 

Answer 1

FALSE!

 

Let a = 3, b = 4, and c = -1

Answer 2

"a,b, and c are real numbers, and a<=b"

 

The rule is that if you multiply both sides of an inequality by a negative value, it reverses the sense of the inequality.  So,

     if c<0, then    ac>=bc

 

Select any negative value for c as an example.

Answer 3

If a <= b, then ac <= bc for a zero c or a positive c, but what happens with a negative c, c < 0?