Find min value of fn: |-5-x| + |2-x|+|6-x|+10-x|; where x is an integer

• 19
  
  
  | -5 - x | + | 2 - x | + | 6 - x | + | 10 - x |
  which can be written as
  
  | 5 + x | + | x - 2 | + | 6 - x | + | 10 - x | >=
  
  | (5 + x) + (x - 2) + (6 - x) + (10 - x)| = 19.
• 13 years agoHelpfull: Yes(16) No(6)
• 
  The answer is 19. | -5 - x | + | 2 - x | + | 6 - x | + | 10 - x | = | 5 + x | + | x - 2 | + | 6 - x | + | 10 - x | >= | (5 + x) + (x - 2) + (6 - x) + (10 - x)| = 19. This means the minimum can not be 0 or 17, so it is either 19 or 23. Since equality holds when x = 2, 19 is in fact the minimum.
• 13 years agoHelpfull: Yes(5) No(4)
• @MRINAL ACTUALLY IT WILL GIVE 19 AS VALUE BY PUTTING X=2,3,4....... U CAN TRY IT SO ANSWER IS 19
• 13 years agoHelpfull: Yes(3) No(2)
• Can anyone explain this | 5 + x | + | x - 2 | + | 6 - x | + | 10 - x | >=
  why sign of first two || are changed and not of whole statement?
  
• 10 years agoHelpfull: Yes(3) No(1)
• if x=0
  then 5+2+6+10=23
  min value of fn=23
• 13 years agoHelpfull: Yes(1) No(9)
• Each term has a minimum value of zero because of the absolute values.
  So the minimum for the function is zero.
  So the answer is Zero.
• 9 years agoHelpfull: Yes(1) No(2)
• y sign ll not change in |6-x| & |10-x| ?
• 11 years agoHelpfull: Yes(0) No(1)