Question

If |x|+|x-1|+|x-2|+|x-3|=3k where k is an integer then integral values of x is/are​

Answer 1

Given : |x|+|x-1|+|x-2|+|x-3|=3k   k is an integer

To find : integral Value of  x

Solution:

as we need to find integral value of  x

so we will check

x < 0   ,  x  = 1  , x  = 2  ,  x ≥ 3

| x  | = x  is   x  ≥  0   &  - x  if  x < 0

x < 0

=> -x  - ( x - 1 )  -(x - 2)  -(x - 3)  = 3k

=> -4x  = 3k - 6

=> -4x = 3(k -  2)

=> x  =  -3  ,  - 6 , - 9 ...................................    

x = 0

0   + 1  +  2  + 3   = 3k

=> 6 = 3k

=> x = 0  Satisfy

x = 1

1  + 0  +  1 +  2  = 3k

=> 4 = 3k

does not satisfy

x = 2

2  +  1 + 0 + 1   = 3k

=> 4 = 3k

does not satisfy

x   ≥ 3

x + x - 1  + x - 2 + x - 3  = 3k

=> 4x  = 3(k + 2)

=> x =  3 , 6 , 9  

x  =     -3  ,  - 6 , - 9 , ...................................    

x = 0

x =   3  ,   6 ,   9 , ...................................    

=> x =  3n    where n is integer

Learn more:

If f(x) =||x|-1| graph of (x)

https://brainly.in/question/17509624

|x|=-x if x <0 true/false​

https://brainly.in/question/10464643