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maths problem?


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#1 kheewei

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Posted 26 April 2007 - 03:16 AM

Given that "a" is a positive constant, solve the inequality:

l x - 3a l > l x - a l



ok.. i've been staring at this for a while now.. and i have no idea how to do this..
anyone can help me out here?
oh, and the "l l" is the modulus.

=)
i'm sure there are quite a few maths geniuses here in boajjang, right? ><

#2 sennheiserlover

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Posted 26 April 2007 - 04:56 PM

X < 2

| X - 3a | > | X - a

Sub a = 1

| X - 3 | > | X - 1 |

Sub X = 1

| 1 - 3 | > | 1 - 1 |

2 > 0

Though I'm sure you've already thought of this lol. Simple try and error.

Edited by sennheiserlover, 26 April 2007 - 04:57 PM.


#3 Dr. Rockso

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Posted 26 April 2007 - 08:02 PM

wait is modulus the same as absolute value?
If it is then...yeah I think this would be basic algebra
But the problem is that im not sure kheewei would give out an easy question like this, especially since it
says its on a cambridge paper.

So wait, whats a modulus?

Edited by Dr. Rockso, 26 April 2007 - 08:03 PM.


#4 FuTuRiStIc_Man

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Posted 26 April 2007 - 08:19 PM

woh!
what kind of math is this???

#5 jjcb1987

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Posted 26 April 2007 - 09:16 PM

woah!!! dun remember le... XDXD if i can remember my maths i sure help.... XDXD

#6 Evolution

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Posted 26 April 2007 - 10:32 PM

A real, positive quantity that measures the magnitude of some number. For instance, the modulus of a complex number is the square root of the sum of the squares of its components. Often it means, simply, the numerical (“absolute”) value of an algebraic quantity x.

#7 Dr. Rockso

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Posted 26 April 2007 - 11:00 PM

A real, positive quantity that measures the magnitude of some number. For instance, the modulus of a complex number is the square root of the sum of the squares of its components. Often it means, simply, the numerical (“absolute”) value of an algebraic quantity x.


so it is the absolute value...why cant every one use that terminology instead of
modulus; its really confusing because of that. That makes everything easier.

Edited by Dr. Rockso, 26 April 2007 - 11:00 PM.


#8 Evolution

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Posted 27 April 2007 - 01:40 AM

Eh. Math people like to separate themselves from others :)

#9 kheewei

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Posted 27 April 2007 - 02:12 AM

X < 2

| X - 3a | > | X - a

Sub a = 1

| X - 3 | > | X - 1 |

Sub X = 1

| 1 - 3 | > | 1 - 1 |

2 > 0

Though I'm sure you've already thought of this lol. Simple try and error.


erm..
how'd you deduce that x<2 from 2>1?

edit: oh wait, is it becuase when you sub anything larger than 2 for x, it doesn't satisfy the inequality?

edit2:wait, that can't be right either, cause then you'll get a different answer for every a that you substitue in.
here's what i got (and think it's wrong, but now after seeing your solution, think it may, just may be correct)
x < 2a
what do you think?

Edited by kheewei, 27 April 2007 - 02:25 AM.


#10 sennheiserlover

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Posted 27 April 2007 - 06:50 PM

Ya. I think correct ba.

X < 2a seems to fit the equation. Lol.

#11 babet

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Posted 28 April 2007 - 07:37 AM

omg....learned this in highschool......[strains to remember this]........

i think ur supposed to do something to get rid of the absolute values....

l x - 3a l > l x - a l

(x - 3a) < -(x - a) and -(x - 3a) > (x - a)

treat the '>' like an equal sign and solve both...
i THINK its something like this but i ain't too sure.

Edited by babet, 28 April 2007 - 07:57 AM.


#12 LiFe4tRaVeLiNg

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Posted 05 May 2007 - 07:27 PM

wow um im not at this level yet...>_<

#13 paulgars

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Posted 05 May 2007 - 07:51 PM

I did problems like these in highschool, and of course, I forgot about them already.

*sigh* Why can't math be this easy?

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