inequalities with absolute values in them

Cgotchag said:
3< the absolute value of x+4 which is less than <9
3 < | x+4 | < 9

Just ponder the behavior of those absolute values. Either of these will do:

3 < ( x+4 ) < 9 for x > -4

3 < -( x+4 ) < 9 for x < -4

You tell me where I got that -4 and why it is so important.
 
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