I checked with the some of the BANA & NBA Nemeth committees and here is our combined response:
Represent the main line with braille dots as we usually do, but use a tactile method to do the additional lines.
Since the red, blue, and purple lines printed ON the main number line represent each SOLUTION, standard braille format for number lines is appropriate there.
The colors, as you say, are insignificant so they do not need to be identified. Using a tactile method for the other lines will work nicely. I would braille each inequality label aligned above each arrowhead.
Betty, Lindy, Dorothy & Diane