Final answer:
The client shows symptoms and diagnostic results that indicate pneumonia. An elevated heart rate, hypoxemia, and abnormal chest X-ray are significant findings supporting this diagnosis.
Step-by-step explanation:
The client described has several symptoms suggestive of pneumonia, which is an infection of the lungs. The presence of an elevated heart rate, hypoxemia, crackling sounds during breathing, greenish sputum, and a radiographic shadow on the chest X-ray are all clinical signs consistent with this diagnosis. The health care provider's collection of symptoms, use of diagnostic tools like a pulse oximeter and stethoscope, and the ordering of a chest radiograph are standard practices in diagnosing respiratory conditions such as pneumonia.