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why do we use a different approach when the absolute value

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Senior Manager
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why do we use a different approach when the absolute value [#permalink] New post 03 Aug 2007, 12:23
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why do we use a different approach when the absolute value is an inequality?


|x-5| =8

x-5 = -8, x=-3
x-5 =8, x=13


|x-5|<8

x-5<8, x<13

x-5<-8 x<-3 XX wrong!

but instead we do:

-x+5<8>-3

Last edited by anonymousegmat on 03 Aug 2007, 19:33, edited 1 time in total.
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 [#permalink] New post 03 Aug 2007, 18:28
becasue of negative number properties .............
Here relationship gets reversed to maintain validity of the equation. For example -7 is bigger than -8.....so if we want to achieve |x-5|<8>-8
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 [#permalink] New post 03 Aug 2007, 18:29
i mean to achieve |x-5|<8>-8
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Re: absolute value [#permalink] New post 04 Aug 2007, 06:37
anonymousegmat wrote:
why do we use a different approach when the absolute value is an inequality?


|x-5| =8

x-5 = -8, x=-3
x-5 =8, x=13


|x-5|<8

x-5<8, x<13

x-5<-8 x<-3 XX wrong!

but instead we do:

-x+5<8>-3


x < -3 will always be wrong.

|x-5|<8

(x-5) < 8
x < 13

Or , - (x-5) < 8
-x +5 < 8
-x <3> -3
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Re: absolute value [#permalink] New post 07 Aug 2007, 10:55
anonymousegmat wrote:
why do we use a different approach when the absolute value is an inequality?


|x-5| =8

x-5 = -8, x=-3
x-5 =8, x=13


|x-5|<8

x-5<8, x<13

x-5<-8 x<-3 XX wrong!

but instead we do:

-x+5<8>-3


If you are comfortable with visual reasoning, you could try drawing the xy plane and solving there. In many cases, it's much simpler.
Senior Manager
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Joined: 14 Jun 2007
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Re: absolute value [#permalink] New post 07 Aug 2007, 13:31
Andr359 wrote:
anonymousegmat wrote:
why do we use a different approach when the absolute value is an inequality?


|x-5| =8

x-5 = -8, x=-3
x-5 =8, x=13


|x-5|<8

x-5<8, x<13

x-5<-8 x<-3 XX wrong!

but instead we do:

-x+5<8>-3


If you are comfortable with visual reasoning, you could try drawing the xy plane and solving there. In many cases, it's much simpler.


yeah, that is what i ended up doing to "prove" it to myself. :o)
Re: absolute value   [#permalink] 07 Aug 2007, 13:31
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