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?

Answer 1

let me illustrate with an example

suppose we have the statement

8 > 3 , which is true
if I add or subtract any number to this statement the result is still true

e.g. 8+5 > 3+5
13 > 8 , still true !
8-10 > 3-10
-2 > -7 , still true

suppose we multiply by a positive number.
e.g. multiply by 5
8(5) > 3(5)
40 .> 15 , still true

suppose we divide by a positive number.
e.g. divide by 2
8/2 > 3/2
4 > 1.5 , still true

BUT, suppose we multiply by -3
8(-3) > 3(-3)
-24 > -9 , ahhhh, that is false
How can we make it true ??
how about
-24 < -9,

try the same with a division by a negative.