In the book by Billingsley Convergence of Probability Measures at page number 123.
Author stated that $$w'_x(\delta) \leq w_x(2\delta), \ \delta < 1/2.$$
and
$$w_x(\delta) \leq 2w_x(\delta) + j(x)$$
Why this is so? I actually can't visualise the picture of it.
Glimpse of that page:
