Question

if absolute value of x-2 + absolute value of x-8= 6 find the possible values of x​

Answer 1

Answer:

all values from 2 to 8 including 2 and 8

Step-by-step explanation:

suppose  x is less  or equal to 2    

absolute value of x-2 + absolute value of x-8= 6  

2-x       +  8- x     =6

10 -2x = 6

10 -6 =2x

2x = 4

x=2

suppose  x is  greater or equal to 8

absolute value of x-2 + absolute value of x-8= 6

x -2      +     x  - 8     =6

2x -10  = 6

2x = 16

x=8

suppose  x is  between 2 and  8  

absolute value of x-2 + absolute value of x-8= 6  

x -2       + 8 -   x     =6

  6 = 6  

all values are satisfied

all values from 2 to 8 including 2 and 8