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. write and solve the absolute inequality that represtents the range of the number
34 - 8 = 26
34 + 8 = 42
26 </= n </= 42
or
|34 - n| </= 8
To write the absolute inequality that represents the range of the number of pages the student reads per day, we first need to determine the maximum and minimum values that the number of pages can vary from the average.
Given that the student reads an average of 34 pages per day and the number of pages varies by up to 8 pages, we can find the maximum and minimum values as follows:
Maximum value: Average + Variation = 34 + 8 = 42
Minimum value: Average - Variation = 34 - 8 = 26
Therefore, the maximum number of pages the student can read per day is 42, and the minimum is 26.
To write the absolute inequality, we consider the range between the minimum and maximum values:
26 ≤ Number of pages read per day ≤ 42
Now we need to solve this inequality. The solutions would include any number between 26 and 42, including the endpoints.
Therefore, the absolute inequality that represents the range of the number of pages the student reads per day is:
|Number of pages read per day - 34| ≤ 8
This inequality states that the absolute difference between the number of pages read per day and the average (34) must be less than or equal to 8. Any value within this range is a solution.