Solving Inequalities (Solved)

Registered User regular
edited February 2008
Alright, so. I am solving inequalities and what not, and I am finding myself confused but can't find the explanation in the book.

(x-10)(x+12)>0

The solution is {X|x<-12 or x > 10}

Now. To solve this you take you use the zero property to give you the 10 > 0, which I understand.

The problem I am running into is how the x+12=0 which means x=-12 has it's inequality sign reversed.

There is only subtraction by a negative number, which you don't rotate the sign for.

Thank you, my math superiors.

starmanbrand on

Posts

• Registered User regular
edited February 2008
No... if x<-12 (for example let's make it -13) then (x-10)(x+12) = (-13-10)(-13+12) = (-23)(-1) = 23 because you're multiplying two negative numbers.

I don't actually recall how to solve inequalities "correctly" but that is in fact the right answer. Because if x is a negative >-12 you end up with 0 or a negative number, and if x is positive <10 you end up with 0 or a negative again. Basically if x is between -12 and 10 you'll only have a negative number on one set of parenthesis, so the answer will be negative, if x is -12 or 10 you end up with a 0 on one set of parens so the answer is 0, and if x is <-12 or >10 you end up with either 2 negatives or 2 positives which yields >0.

Daenris on
• Registered User regular
edited February 2008
Alright, I think I understand what you are saying. I am going to go work on some more problems and hopefully not be back. Thank you!

starmanbrand on
• Registered User regular
edited February 2008
Easy way to see this is to graph it. You have a quadratic with roots at -12 and 10. So far so good.

Now on your graph you need to figure out which way to shade, test (0,0) and see that you need to shade "outside" the parabola. This is the key thing, you're shading to the left of your root at x=-12, and to the right of the root at x=10.

musanman on
• Registered User regular
edited February 2008
Oh man, it's all so clear now. I guess it was never specifically stated WHY you tested points. I thought that was more of a "check to see if your answer is correct" step, instead of an integral part.

Awesome

starmanbrand on
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