Let a bottle of salad dressing stand on the table for a few hours and you will notice that it has separated into layers. That's because oil is insoluble or is not capable of being dissolved.
Insoluble comes from the Latin insolubilis meaning "that cannot be loosened." When a substance is insoluble, it cannot be dissolved or loosened in water. Similarly, a situation that is insoluble has no hope of being solved. When a marriage is beyond repair and cannot be fixed, it is insoluble.