Complete set of values of x satisfying inequality ||x−1|−5|<2x−5 is

We have, ||x−1|−5|<2x−5∴    2x−5>0⇒     x>52                     (1)Now from (1),     −2x+5<|x−1|−5<2x−5⇒−2x+10<|x−1|<2xCase I : x≥1∴    −2x+1011 and  x>−1⇒    x>11/3                                      (2)Case II : x < 1∴    −2x+10<1−x<2x⇒     x>9 and x>1/3⇒ x>9, not possible as x < 1Therefore, x∈(11/3,∞)