In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?

A score must be at least 20 points above or below the average of 105. Twenty points below is 105 − 20 = 85, and twenty points above is 105 + 20 = 125. Since “at least” includes those boundary scores, eligible scores satisfy p ≤ 85 or p ≥ 125, which is choice D.

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