Inequality having Absolute Value and Constant on its 2 side

295Ja · 2012-08-02 05:05:08

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

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

Thanks

bobbym · 2012-08-02 05:07:00

Hi;

What does this mean:

x/+2

295Ja · 2012-08-02 05:10:35

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

then 2 is added to /8-x/

anonimnystefy · 2012-08-02 05:12:58

Hi 296Ja

Is this what you want:

?

295Ja · 2012-08-02 05:16:11

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

Bob · 2012-08-02 05:26:31

hi 295Ja

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

Bob

295Ja · 2012-08-02 05:28:05

Ok. Thank you!

Bob · 2012-08-02 05:32:06

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

Bob · 2012-08-02 05:44:38

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

295Ja · 2012-08-02 05:55:42

Thank you bob bundy,bobbym and anonimnystefy!

Bob · 2012-08-02 05:58:25

You're welcome.

The graph plotter is here if you need it:

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

Bob

295Ja · 2012-08-02 06:01:40

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

Bob · 2012-08-02 06:06:20

OK. I'm looking forward to that!

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

Bob

295Ja · 2012-08-02 06:09:24

I hope so!:D

anonimnystefy · 2012-08-02 09:59:03

Hi

My work here is negligible.

And, is your avatar a manga character?

295Ja · 2012-08-02 12:53:47

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

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

anonimnystefy · 2012-08-02 12:58:57

Oh okay. Have you ever heard of manga?

295Ja · 2012-08-02 13:04:36

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?

anonimnystefy · 2012-08-02 13:06:30

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

295Ja · 2012-08-02 13:12:10

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.

anonimnystefy · 2012-08-02 13:20:37

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

295Ja · 2012-08-02 13:29:36

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)

anonimnystefy · 2012-08-02 13:35:30

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.

295Ja · 2012-08-02 13:47:15

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!

anonimnystefy · 2012-08-02 13:54:47

Yeah, I think he might like it.

See you soon, I hope.

Math Is Fun Forum

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

Inequality having Absolute Value and Constant on its 2 side

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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