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, thescores dor students who are eligible for tutoring or extension activities?

Answer 1

The correct compound inequality would be p
`\leq`85 OR p
`\geq`125.

In order to find this, we must solve two separate parts of the inequality as if they were separate. First we'll start with the less than portion. We know that p must be AT LEAST 20 points lower than the average. This means that:

p + 20
`\leq` 105 ----> subtract 20 from both sides
p
`\leq`85

Now we would do the same with the opposite direction.

p - 20
`\geq` 105 ----> add 20 to both sides
p
`\geq` 125