Question

in order to be invited to tutoring or extension activities, a students 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?
○ 85 < p < 125
○ 85 ≤ p ≤ 125
○ p < 85 or p > 125
○ p ≤ 85 or p ≥ 125

Explanation:

Step1: Determine the lower bound

The average score is 105, and the score must be at least 20 points lower. So we calculate \(105 - 20 = 85\). Since it's "at least" 20 points lower, the inequality for lower scores is \(p\leq85\).

Step2: Determine the upper bound

The score must be at least 20 points higher than 105. So we calculate \(105 + 20 = 125\). Since it's "at least" 20 points higher, the inequality for higher scores is \(p\geq125\).

Step3: Combine the inequalities

The eligible scores are those that are at least 20 points lower or at least 20 points higher than 105. So we combine the two inequalities from Step1 and Step2, which gives \(p\leq85\) or \(p\geq125\).

Answer:

D. \( p \leq 85 \) or \( p \geq 125 \)