Recently I have been struggling with a problem involving the floor function. The problem is: $$ \lfloor x+5 \rfloor = 3\lfloor x\rfloor-1 $$
I have had a similar question to this however it only involved the floor function on one side of the equation and I was able to set up a pair of inequalities and solve them however I have not been able to do the same for this question.
What I have done so far is attempt the same procedure by solving the equation and then setting up a set of inequalities but have been unable to come up with a reasonable answer. I have also graphed this for clarity but am still unsure what is really going on or how to approach this question.