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.
+128475 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
