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anonymousegmat
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anonymousegmat
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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Andr359
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anonymousegmat
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.
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anonymousegmat
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Andr359
anonymousegmat
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|-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)



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