Question 1: Write the inequality notation for all x that are greater than or equal to 5 and less than 10.

Answer: 5 ≤ x < 10

Question 2: Plot the set of all x satisfying 3 ≤ x < 7 on the grid.

Answer: Students plot on grid

Question 3: If x is in the interval 2 ≤ x < 8, what is the range of possible values for x?

Answer: x can be any number between 2 and 8, including 2 but excluding 8

Question 4: Construct an interval on the grid corresponding to x satisfying a ≤ x < b, where a=4 and b=9.

Answer: Students draw on grid

Question 5: Explain why the interval 0 ≤ x < 5 is different from 0 < x ≤ 5.

Answer: In the first, x can be equal to 5; in the second, x cannot be equal to 5.

Question 6: Given the interval 1 ≤ x < 4, what is the opposite interval that includes all values not in this range?

Answer: x < 1 or x ≥ 4

Question 7: Identify and correct the mistake: An interval is written as 2 < x ≤ 6, but the problem states the interval should include 2 and exclude 6.

Answer: Correct interval: 2 ≤ x < 6

Question 8: Solve for x: 4 ≤ x < 10, if x is an integer.

Answer: x can be 4, 5, 6, 7, 8, or 9

Question 9: A measurement device reports an error interval as 0.1 ≤ x < 0.5. Describe this interval and what it implies about the measurement.

Answer: The measurement error is at least 0.1 and less than 0.5, but not including 0.5.

Question 10: If x is in the interval a ≤ x < b, and b - a = 3, what is the length of the interval?

Answer: 3

Question 11: Challenge: Construct a set of three intervals that cover all real numbers, each described by a ≤ x < b, with no gaps in coverage.

Answer: Example: (-∞, 0), 0 ≤ x < 5, 5 ≤ x < ∞

Question 12: Identify the mistake: The interval 3 < x < 7 was written as the solution to a problem, but the notation should be a ≤ x < b. Correct it.

Answer: Corrected interval: 3 ≤ x < 7