Solve the Inequality

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- Feb 15th 2008, 04:35 PMOzzManSolve the inequality
Solve the Inequality

- Feb 15th 2008, 05:54 PMmr fantastic
I always like to

*see*what's going on with these sorts of equations before I get lost in the algebra.

So here's what I'd do:

Draw a graph of . It's easy to do .... just draw and reflect in the x-axis the part below the x-axis. Don't be too fussed about where the x-intercepts are, by the way - they are unimportant.

Now draw a graph of .

It should be easy now to see that the line y = 2 cuts at four points. If you know the x-coordinates of those four points you can easily construct the intervals over which .....

You can see from the graph when you want to solve and when you want to solve in order to get those x-intercepts. - Feb 15th 2008, 06:00 PMOzzMan
Quick question. Where exactly did you get from?

- Feb 15th 2008, 06:04 PMmr fantastic
- Feb 15th 2008, 06:07 PMmr fantastic
- Feb 15th 2008, 06:08 PMOzzMan
I'll show you an example of how I solved this other inequality. Maybe you can tell me if the solving method I used for it is somewhat similar to the first inequality I listed.

- Feb 15th 2008, 06:27 PMmr fantastic
This is a simple

*linear*inequality. In some ways it essentially boils down to what I've suggested, but I think you're applying the method in a superficial way - without really understanding*why*it works. That will cause trouble when ......

Things get more complicated with*quadratic*inequalities. Are you having trouble applying the method I suggested? - Feb 15th 2008, 06:38 PMOzzMan

Thats basically the work I have done for this problem. Hows it look? - Feb 15th 2008, 06:43 PMmr fantastic
- Feb 15th 2008, 06:48 PMOzzMan
Yea I think so. Is there a way to know which way the inequality signs are facing other than graphing? Or is graphing the easiest. I'm all for the easiest method.

- May 13th 2008, 05:18 PMKrizalid
(I know it's late to post but I leave another way, and of course, it may help someone else.)

Inequality equals Consider the left inequality and rearrange it to From here we have First solution

Let's check the another inequality. (Which is easier to tackle.) Hence, our final solution will be given by (here we only need the axis for better understanding)