11-|2x-5|>6 can be split into two inequalities:
(1) 11-(2x-5)>6 (provided 2x-5≥0, that is, x≥5/2) and (2) 11-(5-2x)>6 (provided 5-2x>0, that is, x<5/2).
(1) 11-2x+5>6, 10>2x, 5>x, that is, x<5. So 5/2≤x<5;
(2) 11-5+2x>6, 2x>0, x>0. So 0<x<5/2.
Let's test 11-|2x-5|>6 for 5/2≤x<5. Let x=5/2, then we have 11>6✔️ Let x=4.9, then we have 6.2>6✔️
Now test 11-|2x-5|>6 for 0<x<5/2. Let x=0.1, then we have 6.2>6✔️ Let x=2.4, then we have 10.8>6✔️
But 5/2≤x<5 and 0<x<5/2 can be combined because they show continuity: 0<x<5 is the solution.