Question

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?

85 < p < 125
85 ≤ p ≤ 125
p < 85 or p > 125
p ≤ 85 or p ≥ 125

Answer 1

"At least 20 points higher or lower" means |p − 105| ≥ 20. Solving gives p − 105 ≥ 20 or p − 105 ≤ −20, so p ≥ 125 or p ≤ 85.

Answer: p ≤ 85 or p ≥ 125.