Final answer:
When assessing an injured extremity, the most important thing to check for is a thorough neurovascular exam, assessing the blood flow and nerve function of the injured limb.
Step-by-step explanation:
When assessing an injured extremity, such as the left arm in this case, the most important thing to check for is a thorough neurovascular exam (C).
A neurovascular exam assesses the blood flow and nerve function of the injured limb, ensuring that there is adequate circulation and function. This involves checking the pulses, capillary refill, sensation, and movement of the arm.
Checking for compartment syndrome (A) is also important, but it is typically done after the neurovascular exam. Compartment syndrome is a serious condition that occurs when increased pressure within a muscle compartment impairs blood flow.