Question

Explain why graphing the solutions of an inequality is more efficient than listing all the solutions of the inequality.

Answer 1

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.

Answer 2

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.