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# Inequality involving absolute values

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Intern
Joined: 25 Jul 2007
Posts: 46
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Inequality involving absolute values [#permalink]  08 Nov 2007, 16:14
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?
VP
Joined: 10 Jun 2007
Posts: 1463
Followers: 6

Kudos [?]: 143 [1] , given: 0

Re: Inequality involving absolute values [#permalink]  08 Nov 2007, 16:35
1
KUDOS
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1
Intern
Joined: 25 Jul 2007
Posts: 46
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: Inequality involving absolute values [#permalink]  08 Nov 2007, 18:26
bkk145 wrote:
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1

For the second part of the solution, when a<0, b>0 shouldn't the equation be -a>b instead of -a<b as mentioned by you. If your equation holds then for a=-1 and b=2, |a|>|b| doesn't hold.
VP
Joined: 10 Jun 2007
Posts: 1463
Followers: 6

Kudos [?]: 143 [0], given: 0

Re: Inequality involving absolute values [#permalink]  08 Nov 2007, 18:46
english_august wrote:
bkk145 wrote:
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

There will be two solutions to this...
a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a<b => a>-b, which is same as #2

a<0, b<0
Ans: -a<-b => a>b, which is same as #1

For the second part of the solution, when a<0, b>0 shouldn't the equation be -a>b instead of -a<b as mentioned by you. If your equation holds then for a=-1 and b=2, |a|>|b| doesn't hold.

Yep, you are absolutely right. Careless mistake on my part. You caught one mistake, I caught another of my own. There will be four solutions to
|a|>|b|

a>0, b>0
Ans: a>b

a>0, b<0
Ans: a>-b

a<0, b>0
Ans: -a>b => a<-b

a<0, b<0
Ans: -a>-b => a<b
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 578 [0], given: 19

Re: Inequality involving absolute values [#permalink]  08 Nov 2007, 20:38
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

|a|>|b|

1. if a and b both are +ve: a > b.
2. if a and b both are -ve: a < b.
3. if a is +ve and b is -ve: a > b.
4. if a is -ve and b is +ve: a < b.

so we have two positions: 1. a > b and a < b
CEO
Joined: 29 Mar 2007
Posts: 2585
Followers: 17

Kudos [?]: 244 [0], given: 0

Re: Inequality involving absolute values [#permalink]  08 Nov 2007, 21:27
english_august wrote:
How does one solve this?

|a|>|b|

Intuitively, I know how this inequality will be represented on the number line. But what's the algebric way to solve this, that is, how to represent this inequality without the absolute values?

if a>0 b>0

a>b

if a>0 and b<0>-b

if a<0 & b<0>-b --> a<b

if a<0>0

-a>b a<-b.
Re: Inequality involving absolute values   [#permalink] 08 Nov 2007, 21:27
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