Final answer:
In patients with liver failure, assessing for signs of bleeding is the highest priority due to the potential for coagulopathy that can lead to bleeding complications.
Step-by-step explanation:
When assessing a client with liver failure, the highest priority is assessing for signs of bleeding. Patients with liver failure are at high risk for bleeding due to potential coagulopathy—a condition where the blood's ability to clot is impaired—stemming from the liver's inability to synthesize clotting factors. Monitoring blood pressure hourly and auscultating for bowel sounds are also important but secondary to ensuring the client is not actively bleeding. Deep vein thrombosis (DVT) risk is also a concern in immobilized patients, but it is not the immediate priority in the context of liver failure.