Question 1: Write the interval notation for all x such that x is greater than or equal to 3 and less than 7.

Answer: 3 ≤ x < 7

Question 2: Plot the graph of the interval 5 ≤ x < 9 on the grid.

Answer: Student draws the interval on the grid

Question 3: Construct a triangle with side lengths corresponding to x-values in the interval 2 ≤ x < 6.

Answer: Student draws the triangle on grid with sides between 2 and 6 units

Question 4: Identify the error in the statement: "x > 1 ≤ x < 4".

Answer: Incorrect notation; should be 1 ≤ x < 4

Question 5: If x is in the interval 0 ≤ x < 5, what is the maximum possible value of x?

Answer: Just less than 5

Question 6: Solve for x: 4 ≤ x < 10 and x is an integer.

Answer: x = 4, 5, 6, 7, 8, 9

Question 7: A temperature range is given as 20 ≤ T < 30 degrees. Is 30 degrees included? Explain.

Answer: No, because the interval is less than 30, not less than or equal

Question 8: Express the interval where x is less than 8 but greater than or equal to 2 using notation.

Answer: 2 ≤ x < 8

Question 9: Identify the mistake: "a ≤ x < b" is written as "a < x ≤ b" in a problem. What is the difference?

Answer: The original notation means x includes a but not b; the mistaken version reverses the inequalities

Question 10: Challenge: Find an interval notation for x such that x is greater than 2 and less than 10, but x cannot be exactly 7.

Answer: 2 ≤ x < 7 or 7 < x < 10

Question 11: Explain why the interval 3 ≤ x ≤ 7 does not match the notation a ≤ x < b. What is different?

Answer: Because 3 ≤ x ≤ 7 includes x = 7, which is not part of a ≤ x < b