Posted by Crystal on Tuesday, July 14, 2009 at 9:42am.
see my final reply to
http://www.jiskha.com/display.cgi?id=1247546252
Why is is greater than or = to? I got the answer as being < or = 3500? Can you please explain? Thanks!
Yes, I had agreed that you were right,
and changed it to ≤
here is the corrected version
.04x + 720 - .06x ≥ 650
-.02x ≥ -70
x ≥ -70/-.02
x ≤ 3500
So basically the > = stay the same for the first 2 lines and change to < = for the last? How does that work?
Ok, I will illustrate with an example
e.g.
8 > 5 -----> True
if we add any number or subtract any number the statement is still true
8+6 > 5+6 ---> True
let's multiply by a positive number
8(4) > 5(4) -----> still True !
how about dividing by a positive
8/2 > 5/2 ??? Yes, still True
how about multiplying by a negative
8(-3) > 5(-3) or
-24 > -15 BUT THAT IS FALSE !!!
how do we make it true? We reverse the sign
-24 < -15 , now it's Truee
same thing for division by a negative.
So, in summary,
you can add/subtract any value just like for equations and the inequality sign stays the same.
Same is true for multiplying/dividing by a positive number.
BUT, when you multiply or divide by a negative number in an inequality, you have to reverse the inequality sign at that step. Usually this will be your last step.
Thank you! This is a great review of this topic! Thanks again!