Given: |x−2|+|x−8|=8
Case 1: For x<2
−(x−2)−(x−8)=8
−x+2−x+8=8
−2x+10=8
−2x=−2
⇒ x=1
Case 2: For 2≤x<8
(x−2)−(x−8)=8
x−2−x+8=8
6=8 No solution
Case 3: For x≥8
x−2+x−8=8
2x−10=8
2x=18
⇒ x=9
Hence, the values of x are 1 and 9.