Final answer:
Nursing interventions should address the client's shortness of breath, cough, elevated WBC count, and high PCO₂ level, which are indicative of a respiratory issue such as pneumonia.
Step-by-step explanation:
The three findings in the client's medical record that require nursing intervention are the shortness of breath and productive cough with yellow mucus, increased white blood cell (WBC) count indicating a possible infection, and abnormal blood gas values showing elevated PCO₂ which suggests possible respiratory acidosis or inadequate ventilation. These symptoms and lab results are indicative of a respiratory condition such as pneumonia, which aligns with the findings of crackles in the posterior lungs and an increased opacity noted in the chest x-ray. Nursing interventions would include monitoring the client's respiratory status, ensuring supplemental oxygen is administered as ordered, and assisting with expectoration of mucus.