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

You are not logged in.

## #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

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,802

### 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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

## #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/

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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!

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

### 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

Offline

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

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

Ok. Thank you!

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

### 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

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

### 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

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

Offline

## #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!

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

### 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

Offline

## #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.

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

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

OK.  I'm looking forward to that!

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

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

Offline

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

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

I hope so!:D

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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)

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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?

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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.

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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)

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

### 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.

Offline

## #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!
Bye-bye for now and until next time!

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,015

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

Yeah, I think he might like it.

See you soon, I hope.

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.

Offline