Solve |4y + 1| < |2y - 3| - 7
4y+1>=0 when y>= -1/4 = -0.25
2y-3>=0 when y>= 1.5
so you have three regions you must solve for
y< -0.25 -0.25 <= y < 1.5 and y>=1.25
set up the correct equation (without absolute signs) for each of those and solve them.