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

Answer: 3 ≤ x < 7

Question 2: If x satisfies 5 ≤ x < 10, what is the interval notation?

Answer: 5 ≤ x < 10

Question 3: Plot the graph of the interval 2 ≤ x < 6 on the grid.

Answer: Student draws a line starting at 2 (filled circle) ending just before 6 (open circle).

Question 4: Construct a triangle with sides corresponding to the interval 4.5 ≤ x < 7.5 on the grid. Label the points.

Answer: Student draws a segment from 4.5 to 7.5 with open circle at 7.5, filled circle at 4.5.

Question 5: Simplify the notation: a ≤ x < b, where a=2, b=5. Is 2 included? Is 5 included?

Answer: Yes, 2 is included (closed). No, 5 is not included (open).

Question 6: If x satisfies 1 < x ≤ 4, write the interval notation and identify whether it uses ≥ or > symbols appropriately.

Answer: 1 < x ≤ 4

Question 7: A number x is in the interval 3 ≤ x < 8. Is 3 in the interval? Is 8? Explain.

Answer: Yes, 3 is included. No, 8 is not included, because of the open interval at 8.

Question 8: Identify the common mistake: students write x < 5 when the interval is 2 ≤ x < 5. What's wrong and how to correct it?

Answer: They omitted the 2 ≤ part; correct notation is 2 ≤ x < 5.

Question 9: Given the interval 0 < x ≤ 3, write the notation and describe whether 0 is included.

Answer: 0 < x ≤ 3, 0 is not included (open at 0).

Question 10: Challenge: If x is in the interval 1.5 ≤ x < 4.5, find the midpoint of this interval.

Answer: Midpoint is (1.5 + 4.5)/2 = 3

Question 11: Explain why the notation a ≤ x < b is useful in representing errors or tolerances in measurements.

Answer: It precisely captures the range where measurements are considered acceptable, excluding the upper boundary.