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?
Math - Reiny, Tuesday, May 19, 2009 at 10:17pm
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?
-3x = 9
divide both sides by -3
x = -3
(you did notice that I turned = around to = , didn't you??)