# Solving Inequalities

## Solving Inequalities

find the solution set for :

|2x+9| <= |x-6|

sidenotes - <= means greater or equal to. and " | | " means absolute value.

Thanks

|2x+9| <= |x-6|

sidenotes - <= means greater or equal to. and " | | " means absolute value.

Thanks

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 22

Location : ubseikastan

## Re: Solving Inequalities

Something like a<=|b| is equivalent to the inequalities -b<=a<=b. So, we can treat |2x+9| as a:

-x+6 <= |2x+9| <= x-6

Then, we can repeat the process for the |2x+9| <= x-6 side (we only need to do one side because the process will give the same inequalities each time since two absolute value graphs of lines whose "V" intersection point is on the x axis can only intersect at most two times - the maximum and minimum values we get from one side are these two intersections).

|2x+9| <= x-6

treat x-6 as "a" in a<=|b| this time:

-2x-9 >= x-6 >= 2x+9

so, solving each side, -2x-9 >= x-6 and x-6 >= 2x+9, gives -15<=x<=-1

-x+6 <= |2x+9| <= x-6

Then, we can repeat the process for the |2x+9| <= x-6 side (we only need to do one side because the process will give the same inequalities each time since two absolute value graphs of lines whose "V" intersection point is on the x axis can only intersect at most two times - the maximum and minimum values we get from one side are these two intersections).

|2x+9| <= x-6

treat x-6 as "a" in a<=|b| this time:

-2x-9 >= x-6 >= 2x+9

so, solving each side, -2x-9 >= x-6 and x-6 >= 2x+9, gives -15<=x<=-1

**bfrsoccer**- Administrator
- Posts : 61

Join date : 2008-11-09

## Re: Solving Inequalities

bravo, thanx

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 22

Location : ubseikastan

## Re: Solving Inequalities

actually, I have some questions...

Secondly,

Thanks for helping

i don't get that really, could you clarify/prove?Something like a<=|b| is equivalent to the inequalities -b<=a<=b. So, we can treat |2x+9| as a:

-x+6 <= |2x+9| <= x-6

Secondly,

I really don't understand that... a visual perhaps?(we only need to do one side because the process will give the same inequalities each time since two absolute value graphs of lines whose "V" intersection point is on the x axis can only intersect at most two times - the maximum and minimum values we get from one side are these two intersections).

Thanks for helping

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 22

Location : ubseikastan

## Re: Solving Inequalities

"i don't get that really, could you clarify/prove?" -> Actually...my explanation really doesn't make sense. I got mixed up with where I put the absolute value.

You can think of the absolute value as meaning the "magnitude" of a number, or how far away from it is to zero. So, if |a|<=b (

"I really don't understand that... a visual perhaps?" -> - each two distinct functions only intersects the other twice. Between these intersections is where one is greater than or equal to another.

You can think of the absolute value as meaning the "magnitude" of a number, or how far away from it is to zero. So, if |a|<=b (

*not a<=|b|*), then -b<=a<=b (also, if |a|>=b, then a>=b*or*a<=-b). My answer is still correct, but I can re-solve it using my new explanation as a guide if it's unclear."I really don't understand that... a visual perhaps?" -> - each two distinct functions only intersects the other twice. Between these intersections is where one is greater than or equal to another.

Last edited by bfrsoccer on Thu Mar 26, 2009 9:40 pm; edited 2 times in total

**bfrsoccer**- Administrator
- Posts : 61

Join date : 2008-11-09

## Re: Solving Inequalities

I am very disappointed that you don't know how to embed that image, bfr.

**funion987**- Administrator
- Posts : 146

Join date : 2008-11-09

## Re: Solving Inequalities

Way to not make it with a transparent background.

**funion987**- Administrator
- Posts : 146

Join date : 2008-11-09

## Re: Solving Inequalities

si, si, gracais muchas

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 22

Location : ubseikastan

## Term papers

That's called an inequality. So if we want to solve this, we're going to solve for x, that means get x alone. Solve for x means isolate x.

Term Papers

Term Papers

**albertwilson**- Posts : 9

Join date : 2010-07-19

## Re: Solving Inequalities

'Historic' turnout in Ivory Coast's presidential poll

Voters wait in line to cast their ballot in the first round of presidential elections in Abidjan, Ivory Coast, 31 November There were long lines at some polling stations for the first presidential election in 10 years

Ivory Coast's electoral commission has said that turnout in Sunday's presidential election was "about 80%", describing it as "historic".

The head of the UN mission in the West African country said turnout was among the highest ever seen on the continent.

Nearly 6m people were eligible to vote in the poll, aimed at reuniting the nation after eight years of division.

There are three front-runners for the presidency, including incumbent Laurent Gbagbo. Results are due on Wednesday.

The BBC's John James in Abidjan says people are desperate to find out who their next leader will be and relieved that the poll went smoothly.

Continue reading the main story

Related stories

* Will Ivorian party spirit end the coups?

* Country profile: Ivory Coast

* Delayed Ivorian campaign begins

Ivory Coast, one of the world's main cocoa producers, used to be West Africa's richest country until political unrest sparked by a coup against Mr Bedie in 1999.

The country has been divided in two since northerners took up arms in 2002.

'Exit strategy'

"We are at a turnout rate of about 80%, which historic," the Vice-President of Ivory Coast's Independent Electoral Commission, Mamadou Gnenema Coulibaly, said on Monday.

He added that such a result should "be the pride of everybody taking part in the electoral process".

Continue reading the main story

Landmark Elections

Map

* Polling stations: 20,073

* Polling staff: 60,000

* Registered voters: 5.7m

* Presidential candidates: 14

* Front runners: Laurent Gbagbo (LMP), Henri Konan Bedie (PDCI-RDA), Alassane Ouattara (RDR)

* Ex-rebel leader Guillaume Soro, now interim prime minister, too young to run at 38

* European Union observers on the ground: 120

* UN peacekeepers: 8,500

* Ivorian election tour

* Ivorian tax-free rebel city flourishes

In the country's first presidential election in a decade, President Gbagbo faces 13 rivals.

Former Prime Minister Alassane Ouattara, who is popular in the north and ex-President Henri Konan Bedie, from the party which governed the country for almost 40 years, are seen as Mr Gbagbo's strongest challengers.

In a BBC interview, UN Ivory Coast mission head Young-jin Choi congratulated Ivorians for their discipline during the Sunday's voting.

He pointed out that Ivory Coast was hugely important for the rest of West Africa, as it is the largest economy in the group of former French colonies which share a common currency, the CFA franc.

Mr Choi also said that a successful election could pave the way for the 8,500 peacekeepers to withdraw.

"We are confident, once this election is over peacefully and democratically, if we can deal with other issues quickly, then we can envisage an exit strategy," he told the BBC's Newshour programme.

Unrest fears

There were some reports of delays but voting was otherwise said to have been peaceful and turnout appears to have been good.

Representatives of the major candidates have praised the poll.

"We are on the right track," said Abdoul Toure of Mr Ouattara's RDR party, dismissing fears of violence.

Our reporter says there is optimism that people will react well to the results - unless there is evidence of fraud.

The poll has been postponed six times since 2005, when Mr Gbagbo's five-year mandate officially came to an end, amid rows over rebel disarmament and voter registration.

Although the New Forces rebels signed a peace deal with Mr Gbagbo in 2007, they still control the largely Muslim north, where many people say they faced discrimination under both Mr Gbagbo and Mr Bedie.

If no candidate manages to secure an outright victory, a second round will be held later this month.

All three main contenders believe they will win, raising fears of unrest when the results come through.

Many of the candidates for the top job have similar policies: relaunching the economy, reducing youth unemployment and stopping further conflict.

The delay in organising elections since the 2007 peace deal has put investments on hold, as well as postponing reforms of the cocoa industry which produces nearly 40% of the world's supply of the raw ingredient for chocolate.

_________________________________________________________________________________________________________________________________________________

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Voters wait in line to cast their ballot in the first round of presidential elections in Abidjan, Ivory Coast, 31 November There were long lines at some polling stations for the first presidential election in 10 years

Ivory Coast's electoral commission has said that turnout in Sunday's presidential election was "about 80%", describing it as "historic".

The head of the UN mission in the West African country said turnout was among the highest ever seen on the continent.

Nearly 6m people were eligible to vote in the poll, aimed at reuniting the nation after eight years of division.

There are three front-runners for the presidency, including incumbent Laurent Gbagbo. Results are due on Wednesday.

The BBC's John James in Abidjan says people are desperate to find out who their next leader will be and relieved that the poll went smoothly.

Continue reading the main story

Related stories

* Will Ivorian party spirit end the coups?

* Country profile: Ivory Coast

* Delayed Ivorian campaign begins

Ivory Coast, one of the world's main cocoa producers, used to be West Africa's richest country until political unrest sparked by a coup against Mr Bedie in 1999.

The country has been divided in two since northerners took up arms in 2002.

'Exit strategy'

"We are at a turnout rate of about 80%, which historic," the Vice-President of Ivory Coast's Independent Electoral Commission, Mamadou Gnenema Coulibaly, said on Monday.

He added that such a result should "be the pride of everybody taking part in the electoral process".

Continue reading the main story

Landmark Elections

Map

* Polling stations: 20,073

* Polling staff: 60,000

* Registered voters: 5.7m

* Presidential candidates: 14

* Front runners: Laurent Gbagbo (LMP), Henri Konan Bedie (PDCI-RDA), Alassane Ouattara (RDR)

* Ex-rebel leader Guillaume Soro, now interim prime minister, too young to run at 38

* European Union observers on the ground: 120

* UN peacekeepers: 8,500

* Ivorian election tour

* Ivorian tax-free rebel city flourishes

In the country's first presidential election in a decade, President Gbagbo faces 13 rivals.

Former Prime Minister Alassane Ouattara, who is popular in the north and ex-President Henri Konan Bedie, from the party which governed the country for almost 40 years, are seen as Mr Gbagbo's strongest challengers.

In a BBC interview, UN Ivory Coast mission head Young-jin Choi congratulated Ivorians for their discipline during the Sunday's voting.

He pointed out that Ivory Coast was hugely important for the rest of West Africa, as it is the largest economy in the group of former French colonies which share a common currency, the CFA franc.

Mr Choi also said that a successful election could pave the way for the 8,500 peacekeepers to withdraw.

"We are confident, once this election is over peacefully and democratically, if we can deal with other issues quickly, then we can envisage an exit strategy," he told the BBC's Newshour programme.

Unrest fears

There were some reports of delays but voting was otherwise said to have been peaceful and turnout appears to have been good.

Representatives of the major candidates have praised the poll.

"We are on the right track," said Abdoul Toure of Mr Ouattara's RDR party, dismissing fears of violence.

Our reporter says there is optimism that people will react well to the results - unless there is evidence of fraud.

The poll has been postponed six times since 2005, when Mr Gbagbo's five-year mandate officially came to an end, amid rows over rebel disarmament and voter registration.

Although the New Forces rebels signed a peace deal with Mr Gbagbo in 2007, they still control the largely Muslim north, where many people say they faced discrimination under both Mr Gbagbo and Mr Bedie.

If no candidate manages to secure an outright victory, a second round will be held later this month.

All three main contenders believe they will win, raising fears of unrest when the results come through.

Many of the candidates for the top job have similar policies: relaunching the economy, reducing youth unemployment and stopping further conflict.

The delay in organising elections since the 2007 peace deal has put investments on hold, as well as postponing reforms of the cocoa industry which produces nearly 40% of the world's supply of the raw ingredient for chocolate.

_________________________________________________________________________________________________________________________________________________

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online casinos

**nirvana**- Posts : 18

Join date : 2010-08-19

## Re: Solving Inequalities

bfrsoccer wrote:Something like a<=|b| is equivalent to the inequalities -b<=a<=b. So, we can treat |2x+9| as a:

-x+6 <= |2x+9| <= x-6

Then, we can repeat the process for the |2x+9| <= x-6 side (we only need to do one side because the process will give the same inequalities each time since two absolute value graphs of lines whose "V" intersection point is on the x axis can only intersect at most two times - the maximum and minimum values we get from one side are these two intersections).

|2x+9| <= x-6

treat x-6 as "a" in a<=|b| this time:

-2x-9 >= x-6 >= 2x+9

so, solving each side, -2x-9 >= x-6 and x-6 >= 2x+9, gives -15<=x<=-1

thanks for sharing this great info

**sfhdweb**- Posts : 1

Join date : 2011-01-10

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