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# why do we use a different approach when the absolute value

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why do we use a different approach when the absolute value [#permalink]

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03 Aug 2007, 12:23
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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!

-x+5<8>-3

Last edited by anonymousegmat on 03 Aug 2007, 19:33, edited 1 time in total.
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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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03 Aug 2007, 18:29
i mean to achieve |x-5|<8>-8
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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!

-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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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!

-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
Joined: 14 Jun 2007
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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!

-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. )
Re: absolute value   [#permalink] 07 Aug 2007, 13:31
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