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
26<n<42
|n-34| <= 8
a. The absolute value inequality that represents the range of the number of pages she reads per day can be written as:
|pages - 34| ≤ 8
b. To solve the inequality, we need to consider two cases: when the expression inside the absolute value is positive, and when it is negative.
Case 1: pages - 34 ≥ 0
In this case, the inequality becomes: pages - 34 ≤ 8
Solving this, we get: pages ≤ 42
Case 2: pages - 34 < 0
In this case, the inequality becomes: -(pages - 34) ≤ 8
Expanding and simplifying, we get: -pages + 34 ≤ 8
Rearranging the terms, we have: pages ≥ 26
Combining the two cases, the solution to the inequality is: 26 ≤ pages ≤ 42.
a. To represent the range of the number of pages the student reads per day, we need to consider the deviation from the average of 34 pages. Since the deviation can be up to 8 pages in either direction, we can use an absolute value inequality.
Let x represent the number of pages read per day. The inequality can be written as:
| x - 34 | ≤ 8
b. To solve the inequality, we need to consider two cases: one where the difference between x and 34 is less than or equal to 8, and another where the difference is greater than or equal to negative 8.
Case 1: x - 34 ≤ 8
Adding 34 to both sides, we get:
x ≤ 42
Case 2: x - 34 ≥ -8
Adding 34 to both sides, we get:
x ≥ 26
Combining both cases, we have the solution:
26 ≤ x ≤ 42
Therefore, the student reads between 26 and 42 pages per day, inclusive.