Question

A student reads an average of 34 pages per day. The number of pages she reads per day varies from the average by up to 8 pages. a. Write an absolute value inequality that represents the range of the number of pages she reads per day. b. Solve your inequality.​

Answer 1

The absolute value inequality that represents the range of the number of pages the student reads per day is |x - 34| ≤ 8. Solving this, we find that the student reads between 26 and 42 pages daily.

Step-by-step explanation:

To write an absolute value inequality that represents the range of the number of pages the student reads per day, we consider the average pages read (34 pages) and the maximum variation allowed (8 pages above or below the average).

The absolute value inequality is:

|x - 34| ≤ 8

To solve this inequality, we need to consider the two scenarios that can satisfy the absolute value expression:

1. x - 34 ≤ 8 (The number of pages read is within 8 pages above the average)

2. x - 34 ≥ -8 (The number of pages read is within 8 pages below the average)

Solving both we get:

1. x ≤ 42 (The student reads up to 42 pages)

2. x ≥ 26 (The student reads at least 26 pages)

Therefore, the range of pages the student reads per day is from 26 to 42 pages.