Question

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's illustrate it with a number example

hope you agree that

8 > 3

You can add or subtract the same number to both sides of the inequation and the statement would still be true, right?

now multiply both sides by any positive number
e.g. 8(5) > 3(5)
40 > 15 , still true ? YES

now multiply both sides by a negative number.

e.g. 8(-2) > 3(-2)
-16 > -6 , is this true ? NOOOOO!
how do we make it true?
how about turning the > to <

-16 < -6

Do we do the same thing for equations you ask?

how about
-3x = 9
divide both sides by -3
x = -3

(you did notice that I turned = around to = , didn't you??)