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Question:
On any given day, the number of users, u, that access a certain website can be represented by the inequality |125-u|<=30. Which of the following represents the range of users that access the website each day?
Answer:
The range of users that access the website each day is 95 ≤ u ≤ 155.
Step-by-step explanation:
1. Understand the given inequality: |125-u| ≤ 30
2. Recall that for any absolute value inequality |x| ≤ a, it can be written as -a ≤ x ≤ a
3. Apply this to our inequality:
-30 ≤ 125-u ≤ 30
4. Solve the left side of the inequality:
-30 ≤ 125-u
-30 - 125 ≤ -u
-155 ≤ -u
u ≤ 155
5. Solve the right side of the inequality:
125-u ≤ 30
-u ≤ -95
u ≥ 95
6. Combine the results from steps 4 and 5:
95 ≤ u ≤ 155
Additional information:
This type of problem involves solving an absolute value inequality. The solution gives us a range of values that satisfy the original inequality. In this context, it means that on any given day, the website can expect anywhere from 95 to 155 users, inclusive. This information could be useful for planning server capacity, predicting peak usage times, or analyzing user engagement trends.