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Posted by **Crystal** on Tuesday, July 14, 2009 at 9:42am.

-.02x <= -70

x < = -70/-.02

x < = 3500

Or do the sign go the other way like this?

.04x + 720 - .06x > = 650

-.02x > = -70

x > = -70/-.02

x > = 3500

Which would be the solution to solve this inequality?

.04 x + .06(12000-x) >= 650

- Algebra -
**Reiny**, Tuesday, July 14, 2009 at 9:50amsee my final reply to

http://www.jiskha.com/display.cgi?id=1247546252

- Algebra -
**Crystal**, Tuesday, July 14, 2009 at 10:14amWhy is is greater than or = to? I got the answer as being < or = 3500? Can you please explain? Thanks!

- Algebra -
**Reiny**, Tuesday, July 14, 2009 at 10:24amYes, 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

- Algebra -
**Crystal**, Tuesday, July 14, 2009 at 11:00amSo basically the > = stay the same for the first 2 lines and change to < = for the last? How does that work?

- Algebra -
**Reiny**, Tuesday, July 14, 2009 at 11:43amOk, 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.

- Algebra -
**Crystal**, Tuesday, July 14, 2009 at 12:06pmThank you! This is a great review of this topic! Thanks again!

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