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 a student's score must be at least 20 points lower. So we calculate \(105 - 20 = 85\). Since it's "at least" 20 points lower, the score \(p\) can be equal to or less than 85, so \(p\leq85\).

Step2: Determine the upper bound

A student's score must be at least 20 points higher than the average. The average is 105, so \(105 + 20 = 125\). Since it's "at least" 20 points higher, the score \(p\) can be equal to or greater than 125, so \(p\geq125\).

Step3: Combine the inequalities

The student is eligible if their score is at least 20 points lower (or equal) OR at least 20 points higher (or equal). So we combine the two inequalities \(p\leq85\) and \(p\geq125\) with the "or" operator, resulting in \(p\leq85\) or \(p\geq125\).

Answer:

\(p\leq85\) or \(p\geq125\) (corresponding to the option: \(p\leq85\) or \(p\geq125\))