Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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

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

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

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,953

Hi;

What does this mean:

x/+2

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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

x/is part of:

/8-x/ (absolute value of 8-x)

then 2 is added to /8-x/

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,795

hi 295Ja

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

Ok. Thank you!

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,795

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,795

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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

Thank you bob bundy,bobbym and anonimnystefy!

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,795

You're welcome.

The graph plotter is here if you need it:

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

Bob

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

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,795

OK. I'm looking forward to that!

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

Bob

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

I hope so!:D

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

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.

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

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!

Bye-bye for now and until next time!

Have a great day ahead!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

Yeah, I think he might like it.

See you soon, I hope.

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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