Question 1: Simplify the interval notation: 3 ≤ x < 7. What does this interval represent?

Answer: x is greater than or equal to 3 and less than 7

Question 2: If x satisfies 0 ≤ x < 10, what is the possible range of x?

Answer: x is from 0 inclusive up to but not including 10

Question 3: Plot the interval 4 ≤ x < 9 on the grid provided.

Answer: Students draw a line starting at 4 (filled circle) and ending before 9 (open circle).

Question 4: Express the interval where 2 < x ≤ 8 in notation.

Answer: x > 2 and x ≤ 8

Question 5: A thermometer shows a temperature between 15°C and 25°C, including 15°C but not 25°C. Write this as an interval.

Answer: 15 ≤ T < 25

Question 6: Identify the mistake: The interval is written as 5 < x ≤ 10, but the problem states that x is at least 5 and less than 10.

Answer: Incorrect notation; should be 5 ≤ x < 10

Question 7: Given the interval a ≤ x < b, if a = 1 and b = 5, what is the set of possible x values?

Answer: x is greater than or equal to 1 and less than 5

Question 8: Solve for x: If x satisfies 6 ≤ x < 12, what is the smallest possible value of x?

Answer: The smallest value x can be is 6

Question 9: A scientist measures a substance’s pH to be between 4 and 7, including 4 but not 7. Write the interval notation and explain what it means.

Answer: 4 ≤ pH < 7; pH is at least 4 and less than 7

Question 10: Construct an interval on the grid where x is greater than 10 but less than or equal to 15.

Answer: Students draw a line starting at 10 (open circle) and ending at 15 (filled circle).

Question 11: Identify the error: The interval written as 3 ≤ x ≤ 7 includes both endpoints, but the problem states x is strictly between 3 and 7.

Answer: Incorrect; should be 3 < x < 7

Question 12: Explain why the interval 0 ≤ x < 0 is invalid and what it actually represents.

Answer: The interval is empty because x cannot be both greater than or equal to and less than 0 at the same time.