1. The sum of all non-negative integer solutions to the inequality $|2 x-1|<6$ with respect to $x$ is $\qquad$ .
2.1.6.
The original inequality is equivalent to $\left\{\begin{array}{l}2 x-1-6 .\end{array}\right.$
Solving it, we get $-\frac{5}{2}<x<\frac{7}{2}$.
Therefore, all non-negative integer solutions that satisfy the condition are $x=0,1,2,3$.
Thus, the sum of all non-negative integer solutions is 6.