Question 1: Express the solution set for all real numbers x such that x is between 3 and 7, including 3 but excluding 7, using the notation a ≤ x < b.

Answer: 3 ≤ x < 7

Question 2: Given the interval 5 ≤ x < 12, calculate the length of this interval.

Answer: 7

Question 3: Plot the graph of y=2x for x in the interval a ≤ x < b, where a=1 and b=4.

Answer: Graph drawn on grid from x=1 to x<4, y=2x

Question 4: Construct a triangle on the grid with side lengths that satisfy the error interval 4 ≤ x < 6 for each side length.

Answer: Any triangle with sides in [4,6), e.g., 4.5, 5, 5.8

Question 5: Explain why the interval 0 ≤ x < 0 does not contain any real numbers.

Answer: Because the interval implies x is greater than or equal to 0 and less than 0 simultaneously, which is impossible.

Question 6: Identify and correct the mistake in interpreting the interval: 2 < x ≤ 5.

Answer: The interval uses < for 2 and ≤ for 5, which is inconsistent with the notation a ≤ x < b.

Question 7: A survey records times from 8:00 ≤ x < 9:00. What is the total time span in minutes?

Answer: 60

Question 8: A data set includes values in the interval 10 ≤ x < 15. Which of these values could be part of the data: 9.9, 10, 14.999, 15?

Answer: 10, 14.999

Question 9: Show how to represent all x such that x is greater than 2 but less than or equal to 7 using the notation.

Answer: 2 < x ≤ 7

Question 10: Identify a common misconception when students interpret the interval 1 ≤ x < 4 and explain how to correct it.

Answer: Some students think x can equal 4, but the notation specifies x is less than 4, not including 4.

Question 11: Given an interval with x in [3, 8), find the midpoint of the interval and explain its significance.

Answer: Midpoint is 5.5, representing the center of the interval