Explanation

Insofar as this question talks about absolute value, we are dealing with the distance from zero. The 100 inside the bars essentially shifts that question so it's oriented not around zero, but how close 7x can get to 100, either above or below it. For example, ifthen and the difference is 30. That's about four or five 7's further away then it could be. If , then. That's a difference from 100 of 5, which I notice is an answer choice. But that can't be the least difference, because if we take off 7, we are at 98, just 2 off from 100. Those are the two closest multiples of 7.

The correct answer is (B).