Algebra 2 question?

The end points are open, so it won't be C or D with the ≤ symbols.

An absolute value is always positive, so it doesn't make sense to compare the absolute value to -3, so B is not the answer.

So the answer is A.

Essentially, that is saying that the distance between x and 1 is less than 4. That makes sense if you look at it. The midpoint of that range is 1, right in the middle. And all points that are on the graph are within 4 units of that point.
| x - 1 | would represent the distance from 1, just like | x | represents the distance of a number from zero. And you want that distance to be less than 4 units away.

Answer:
A. {x ∈ ℝ | |x-1| < 4 }