To solve an absolute value inequality, we can do two things right: make a bunch of cases or graph the thing.
But for a big inequality like: $$||x|^2 - 8|x| + 15 + |x + 1| - |2x - 5| + |x|| < 2$$ we will have to make a lot of cases. I was thinking if there was a faster way of solving these big inequalities?