The saying "A picture is worth a thousand words" comes to mind here. You can list all of the possible points in a solution region, or you can list a few points to give the general pattern. Though this method requires a bit more work than simply graphing and showing the solution shaded region. A visual is often more efficient at conveying a message especially to those who aren't proficient with algebra. I'm sure there are other reasons why graphs are the better choice, but that's all I could think of really.
The number of solutions to an inequality is infinite. You couldn't possibly list them. That's why a graph or set notation has to be used.
examples:
x ≥ 5 The solution set is [5, infinity) in set notation or a graph showing the shaded area above x = 5
two variable ...
y > 2x+1 solution set must be graphed because it's every point above the line y = 2x+1 all the way to infinity.
you can't possibly list all the solutions. Not even for a system of inequalities where the solution set is defined by boundaries can you list all the solutions because there are still an infinite number of points within the bounds.
