From what you have written, I am not quite sure what you are asking.

The equation you gave does in fact have solutions. Because of the nature of the absolute value, any x-value you put into the equation will either result in zero or a positive number, the minimum value being zero. I am certain that you know 0 > -4, so this equation is true for all real values, because, as I just mentioned, any x-value will yield zero or a positive number.