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**Hannibal lecter****Member**- Registered: 2016-02-11
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hello

I tried to solve these two question about absolute value inequality but I stuck with x^2 and with number 2

please see this picture and solve this two for me, the answer of my teacher for 1) is (-∞,1] U [9,∞)

and for 2) is (-∞,∞)

is it right?

I tried the a way that a member learned me that here but I stuck

solve this in short way for me please!!! it takes me 3 days and I didn't find any solution :

*Last edited by Hannibal lecter (2016-12-22 12:07:58)*

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**Hannibal lecter****Member**- Registered: 2016-02-11
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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

For 1) that should be

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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yes and what is the next

I mean I stuck in this point,,, what I have to do now? please I want full solution I really have an exam after one week in such topics..

*Last edited by Hannibal lecter (2016-12-22 15:16:43)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Divide both sides by 3:

Now factor that.

http://www.mathsisfun.com/algebra/inequ … lving.html

http://www.purplemath.com/modules/ineqquad.htm

http://www.wikihow.com/Solve-Quadratic-Inequalities

Can you do the rest?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I think yes, maybe

x-9 ≥ 0 =>>>>>>>>> x≥9 then [9,∞)

and x-1≥0 =>>>> x≥1 then [1,∞)

sol : [9,∞] U [1,∞)

is that right?? but the answer of my teacher is different???,

by the way thank you for this link I study the factors and quadratic equations,

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

The answer of your teacher is different because yours is not correct. Did you read the links thoroughly, they show how to do this.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I was study factoring and Quadratic Equations but I just started to study (Solving Quadratic Inequalities),

and I stuck with the first example,, I'll finish it...

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I finish the first link math isfun.com

is the sol : : [9,∞] ∩ [1,∞)

not U?

and if yes why ∩????

is cause will be either the first interval or the second one??

please I need answers I get board from trying I have a lot of topics in maths to finish

*Last edited by Hannibal lecter (2016-12-23 08:01:24)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I do not use that set notation but I am getting:

The area you want is colored purple.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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but how that can be? x<= 1??

if we put -3 in it will be |-3+3| , zero,, and that is wrong right?

how did you do that

*Last edited by Hannibal lecter (2016-12-23 08:43:36)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

if we put -3 in it will be |-3+3| , zero,, and that is wrong right?

That is correct. I think you should point that out to your teacher.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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sure,,, but what is the right answer now?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Same as before just state that

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I mean how do you solve this ? what is the steps do it here please

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
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1) Find the zeros.

2) Plot them on the number line.

3) Pick a point or points to get the interval you want.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I'll show you what I did,,,

when (x-9) (x-1) ≥ 0

(x-9) = 0 , x=9 the interval is [9,∞) , test a value between this interval : "10" : 10^2 - 10*10 +9 ≥ 0 , +9 ≥ 0 and that is true!

(x-1) ≥ 0 x=1 the interval is [1,∞) , test a value between this interval : "2" : 2^2 - 10*2 +9 ≥ 0 , -7 ≥ 0 , and that is WRONG! so Switch this inequality and become : x ≤ 1 , the interval is : (-∞,1]

sol : (-∞,1] U [9,∞), except -3

is that ok? hehehe

*Last edited by Hannibal lecter (2016-12-23 09:51:48)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

I have not done any of these in 83 years, so forgive me, I am beyond rusty. That is how I would phrase it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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that is ok I'm keeping on, thank you

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
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Okay, work on the next one.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 188
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I try it, it is [9,∞)

and maybe (-∞,9], but I can't chose that one cause it is consist number 3 which make the denominator zero and I'll point this to the teacher,...

please can you give me the end of sol that you get it????

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Are you sure you have copied the problem correctly?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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sorry I don't understand what is copied

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Are you sure you copied the problem down correctly for #2?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Hannibal lecter****Member**- Registered: 2016-02-11
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yes of course

but for the end of sol I don't know what is the truth 100% the sol of teacher or min

anyway I need you solution cause it is always true when you are using the graph

to make sure I'm point to my teacher with a correct information

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