To solve the inequality exactly according to what you show, without x-1 being associated as separate,
x-1/11>1/8
-----using additive inverse
Attempt at representing a graph:
<------------------|----------()=========================|=============>
0 1
The double marking indicates filled-in point and the single marking indicates nonincluded points; the empty parentheses is for the critical value boundary between solution points and nonsolution points. Note that this is a strict inequality, and that is NOT part of the solution.