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How would you solve this?

 

|3x+9|-|1-3x|=|4x-12|-|3x+9|

 

The original question was this:  The terms |1-3x|, |3x+9|, |4x-12| in that order, form an arithmetic sequence. Give the least possible value of x.

 May 20, 2021
 #1
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+1

We have  the  followig 4  possible  systems   and solutions

 

1 - 3x  +  d  =  3x + 9

3x + 9 +  d  =  4x  - 12

 

x = -29/5     d  =  -134/5       (  reject.....d  added  to   abs ( 1 - 3x )   is  negative....but  the  second term, abs (3x + 9), is positive  )

 

3x  - 1  +  d  =  3x + 9

3x + 9  +  d   =  4x - 12

 

x = 31     d  =  10

 

1 - 3x  + d   =  3x + 9

3x + 9  + d  =  12  - 4x

 

x = -5/13    d  =  74/13

 

3x - 1  + d   =  3x + 9

3x + 9 + d  =  12 - 4x

 

x =  -1     d   =  10      (reject....iif  x  = -1, the  terms  would  be  4, 6 , 16....not  arithmetic )

 

The  least possible  value for  x  =  -5/13

 

 

cool cool cool

 May 21, 2021
 #2
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Thank you!

Guest May 21, 2021

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