Homework Help: Algebra

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

.04x + 720 - .06x > = 650
-.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 9:50am
see my final reply to

http://www.jiskha.com/display.cgi?id=1247546252
Algebra - Crystal, Tuesday, July 14, 2009 at 10:14am
Why 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 10:24am
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
Algebra - Crystal, Tuesday, July 14, 2009 at 11:00am
So 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 11:43am
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.
Algebra - Crystal, Tuesday, July 14, 2009 at 12:06pm
Thank you! This is a great review of this topic! Thanks again!

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