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#1 2012-08-02 05:05:08

295Ja
Member
Registered: 2012-07-28
Posts: 39

Inequality having Absolute Value and Constant on its 2 side

Hello everyone!Please give me ideas on how should I solve problems like this one:

                        3/8-x/+2<7-2/x-8/

Thanks smile

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#2 2012-08-02 05:07:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,118

Re: Inequality having Absolute Value and Constant on its 2 side

Hi;

What does this mean:

x/+2


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#3 2012-08-02 05:10:35

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

x/is part of:
/8-x/ (absolute value of 8-x)

then 2 is added to /8-x/

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#4 2012-08-02 05:12:58

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Hi 296Ja

Is this what you want:

?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#5 2012-08-02 05:16:11

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

anonimnystefy: that's exactly what I want. Thank you!

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#6 2012-08-02 05:26:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,182

Re: Inequality having Absolute Value and Constant on its 2 side

hi 295Ja

I've just arrived home and seen this.  Give me a moment and I'll give it a try.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2012-08-02 05:28:05

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Ok. Thank you! smile

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#8 2012-08-02 05:32:06

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,182

Re: Inequality having Absolute Value and Constant on its 2 side

Ok.  Split the problem into three parts.

part (i) suppose x>8

Then x-8 is positive and 8 - x is negative.

So you can replace the absolute values like this

3(x-8) + 2 < 7 - 2(x-8)

so

5(x-8) < 5

x-8 < 1

x < 9

So for part (i)     8 < x < 9

Bob

part two follows soon


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2012-08-02 05:44:38

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,182

Re: Inequality having Absolute Value and Constant on its 2 side

part (ii)

Suppose x < 8

then x-8 is negative and 8 - x is positive.

So I can re-write without absolutes like this:

-3(x-8) + 2 < 7 + 2(x-8)

-5 < 5(x-8)

-1 < x - 8

7 < x

so for part (ii)

7 < x < 8

Finally for part (iii)

If x = 8

the inequality becomes

2 < 7  which is true so x = 8 is also a solution

Putting all together

7 < x < 9

Graph below

Bob

View Image: inequal.gif

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2012-08-02 05:55:42

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Thank you bob bundy,bobbym and anonimnystefy! smile

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#11 2012-08-02 05:58:25

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,182

Re: Inequality having Absolute Value and Constant on its 2 side

You're welcome.

The graph plotter is here if you need it:

http://www.mathsisfun.com/data/function … =-8&ymax=8

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2012-08-02 06:01:40

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Thank you again! I guess I'll be thanking you guys a lot of times more in the near future. big_smile

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#13 2012-08-02 06:06:20

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,182

Re: Inequality having Absolute Value and Constant on its 2 side

OK.  I'm looking forward to that!  smile

On the other hand, maybe you won't need any more help.  up

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2012-08-02 06:09:24

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

I hope so!:D

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#15 2012-08-02 09:59:03

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Hi

My work here is negligible.

And, is your avatar a manga character?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#16 2012-08-02 12:53:47

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

anonimnystefy I'm not sure if my avatar is a manga character.

Last edited by 295Ja (2012-12-02 23:59:07)

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#17 2012-08-02 12:58:57

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Oh okay. Have you ever heard of manga?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#18 2012-08-02 13:04:36

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Yes. I have lot of friends who love to read mangas. By the way, are you refering manga as a comic book or animated film?

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#19 2012-08-02 13:06:30

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Mangas are the comic books and animes are animated films. I like both. Have you read/warched any? I presume you watched Naruto?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#20 2012-08-02 13:12:10

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

I have read and watched only few. I have watched Naruto for a few times and I don't know that much about it. By the way,Naruto is one of the favorite animes that boys watch here.

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#21 2012-08-02 13:20:37

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Here, everybody reads manga or watches anime likes Naruto. There are some other ones I like. Death Note and Inuyasha (my avatar) for example.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#22 2012-08-02 13:29:36

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Same here. I think I'm only one of the few teens who is not yet that hooked in mangas and animes.But last week, I watched Princess Mononoke and I liked it. I have a brother who really love anime. I have heard him telling how good Death Note is. He also liked Fairy Tail and Reborn.

Last edited by 295Ja (2012-12-03 00:34:32)

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#23 2012-08-02 13:35:30

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

I heard Princess Mononoke is good. I have a few manga waiting on my "to read" list (like Fullmetal Alchemist, Princess Mononoke, Hellsing,...), but I will start that when I finish Inuyasha. Death Note is much better as aa manga, but has boring parts.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#24 2012-08-02 13:47:15

295Ja
Member
Registered: 2012-07-28
Posts: 39

Re: Inequality having Absolute Value and Constant on its 2 side

Whooh! Seems like you're an avid reader of mangas.
I'll tell my brother about the Death note's manga.
I'm sorry cause I'm about to log-out now. Its because I'm going to prepare for my class later. It's been nice knowing more of you! big_smile
Bye-bye for now and until next time!
Have a great day ahead! smile

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#25 2012-08-02 13:54:47

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: Inequality having Absolute Value and Constant on its 2 side

Yeah, I think he might like it.

See you soon, I hope. smile


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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