Final answer:
After starting the administration of alprazolam (Xanax), a nurse should prioritize checking the client's blood pressure to monitor for hypotension and also observe for other side effects such as drowsiness and dizziness.
Step-by-step explanation:
The initial action a nurse should take after the administration of alprazolam (Xanax) is started is to check the client's blood pressure. Alprazolam can cause hypotension as a side effect, so it is essential to monitor the patient's blood pressure to assess for any significant changes. Additionally, the nurse should observe for signs of other common side effects including drowsiness, dizziness, and changes in mental status. Regular monitoring helps ensure patient safety and appropriate management of any adverse effects that may arise from the medication.