Question 1: Express the following interval in notation: all real numbers greater than or equal to 3 and less than 7.

Answer: 3 ≤ x < 7

Question 2: Plot the interval 2.5 ≤ x < 4.5 on the grid.

Answer: Students will draw a line on the grid between 2.5 and 4.5, with filled circle at 2.5 and open circle at 4.5.

Question 3: If x is in the interval a ≤ x < b, and a=5, b=10, what is the range of possible values for x?

Answer: 5 ≤ x < 10

Question 4: Construct a triangle with vertices at points corresponding to x-values in the interval 1 ≤ x < 3. Draw it on the grid.

Answer: Students will draw a triangle with base spanning from x=1 to x=3, with vertices marked accordingly.

Question 5: Explain why the notation a ≤ x < b is used to describe an error bound that includes a but does not include b.

Answer: Because the inequality includes a (≤) but excludes b (<), it precisely captures the range starting at a and approaching b without including it.

Question 6: A measurement gives an error interval of 4.2 ≤ x < 4.6. What is the width of this interval?

Answer: 0.4

Question 7: Identify and correct the mistake in this interval notation: 3 < x ≤ 7.

Answer: The interval uses '<' and '≤' incorrectly; the correct notation matching the description should be 3 ≤ x < 7.

Question 8: Given the interval 1.5 ≤ x < 2.5, find the midpoint and explain its significance.

Answer: Midpoint is 2.0; it represents the center of the interval.

Question 9: A student states that x can be exactly 5 in the interval 3 ≤ x < 7. Is this correct? Justify your answer.

Answer: Yes, because the interval includes 3 but does not include 7, so x=5 is within the interval.

Question 10: Challenge: If x is in the interval a ≤ x < b, and the length of the interval is known to be 4, and a=1, what is the value of b?

Answer: b = 5

Question 11: Identify the interval notation for a set of numbers including 0.5, 1, 1.5, but excluding 2.

Answer: 0.5 ≤ x < 2