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What are the solutions for abs(y-2)=1 ?? Its a basic problem

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What are the solutions for abs(y-2)=1 ?? Its a basic problem [#permalink] New post 01 Aug 2007, 12:47
What are the solutions for

abs(y-2)=1 ??

Its a basic problem but I'm getting a different answer from the offical solution. Please go over the math. My solutions are y=3 and 1. The official solutionis y=3 and -1. what am i missing?
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 [#permalink] New post 01 Aug 2007, 12:58
y=-1 is not correct. abs(y-2)=abs(-1-2)=abs(-3)=3.


There are two ways to solve for the correct solution:

(1) Square both sides. This gives: y^2-4y+4=1. So y^2-4y+3=0 and factor out to get (y-3)(y-1)=0 so y=3 and y=1.

(2) y-2=1. So y=3. Also -(y-2)=1. So -y+2=1, or y=1.
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 [#permalink] New post 01 Aug 2007, 13:13
thanks.

...I got what you got but its not the same answer that is posted on Challenge 14.
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 [#permalink] New post 01 Aug 2007, 20:54
I'm also getting y=1 and y=3

:-D
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 [#permalink] New post 01 Aug 2007, 21:06
Absolute values can take positive and negative values.

Postive case:

y-2 = 1 -> y = 3. Fair enough

Negative case:
-y+2 = 1
y = 1.

Here's why -1 is wrong.
If y = -1, then |y-2| = |-1-2| = 3.
  [#permalink] 01 Aug 2007, 21:06
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