inequalities with the unknown in the denominator (1 Viewer)

[kloudsurfer]

As for the original question, Ive always been taught to do it differently. I dont wanna confuse you or anything, I just thought it was strange that im the only one who is taught to do it this way -

The bottom cant equal zero so
5x-2 =/= 0
x=/=2/5

The solve the equation as if it wasnt an inequality and you get x=1, so the two x values are 1 and 2/5.

Then you draw it on a number line (or just do it in your head like i do) and test a point on the line, say 0. So sub 0 in as x, and you get
6/-2<0 which is true, so the point (on the number line if u need it) falls outside the two values. Therefore x<2/5 or x>1.

Whew. So doesnt anyone else do it this way? It saves you drawing a parabola.

 

[SoulSearcher]

I don't use that way, it gets too confusing for me. I prefer the other way, because it's easier for me to understand

 

[~shinigami~]

It saves you drawing a parabola.

*Gasp* I can't believe I'm saying this because I hate any kind of curve sketching but I actually enjoy that part of inequalities the most.

Plus the parabola doesn't have to be very accurate.

It saves you testing points.

 

[Riviet]

The graph is incredibly powerful, many inequalities involving polynomials are often more than degree 2, meaning they really do save time in an exam (instead of testing points).

 

[~shinigami~]

Riviet, your sig is so funny. I laughed so hard at "4 factorial? That's heaps."

 

[kloudsurfer]

Meh, I was just taught to do it that way, everyone else's way is good too. I thought I would answer the question because it is about the only 3U thing that I can do.

Anywhoo, none of this matters to me because i am DROPPING 3U!!!!!!!!!!!!!!!!!!

Ahem. Sorry, I am really happy to get rid of it.

 

[Riviet]

Riviet, your sig is so funny. I laughed so hard at "4 factorial? That's heaps."

Haha thanks, I also laughed at the time I first saw it and still laugh.

 

[SoulSearcher]

Anywhoo, none of this matters to me because i am DROPPING 3U!!!!!!!!!!!!!!!!!!

Ahem. Sorry, I am really happy to get rid of it.

No, it's ok to be happy Yo're dropping a subject which you hate, therefore you should be happy

 

[~shinigami~]

But 3 unit is fun! It involves buying hot chips that are saturated with sweet chilli sauce during the 10 min break and sprinting back across the 4 lane road whilst trying not to drop any chips and also making it back in time before the teacher LOCKS the door. Then proceeding to solve the problem of whether to eat using both hands and not do any work or actually buckle down and do some maths.

Let's just say, my hands are pretty sticky after a good lesson of maths. (Yes, attach all the dirty connotations you want, SoulSearcher. )

 

[SoulSearcher]

Hehehe ... I won't bother. People can figure those ones too easily

Hmm, instead of expanding the brackets out for the original equation, you could go:
6(5x-2) < 2(5x-2)²
2(5x-2)² - 6(5x-2) > 0
(5x-2)[2(5x-2)-6)] > 0
(5x-2)[10x-4-6] > 0
(5x-2)(10x-10) > 0
10(5x-2)(x-1) > 0,
then solve from there.