Question 1: Simplify and write the correct inequality: 3 + 2x ≥ 7.

Answer: x ≥ 2/2 or x ≥ 1

Question 2: If y ≤ 5 and y ≥ 2, what is the range of possible values for y?

Answer: 2 ≤ y ≤ 5

Question 3: Identify the mistake: The inequality 4x + 3 ≥ 7 simplifies to x ≥ 1. Does this correct? Explain.

Answer: No, because 4x + 3 ≥ 7 simplifies to 4x ≥ 4, so x ≥ 1, which is correct. The mistake would be if someone forgot to subtract 3 first.

Question 4: Plot the graph of y ≥ 2x + 1 on the grid.

Answer: Students should draw the line y=2x+1 with a shaded region above or on the line.

Question 5: Construct a triangle on the grid with sides of lengths that satisfy the inequality: side A ≥ side B + side C.

Answer: Sample: A = 6 units, B = 2 units, C = 3 units; verify 6 ≥ 2 + 3 (true).

Question 6: A car travels at a speed v, where v ≥ 30 km/h. If the speed is 45 km/h, is this correct? Why?

Answer: Yes, because 45 ≥ 30. The speed meets the minimum requirement.

Question 7: Solve for x: 5x ≤ 20.

Answer: x ≤ 4

Question 8: In a survey, the number of people who prefer tea is at least 120, but no more than 200. Write this as an inequality.

Answer: 120 ≤ preference ≤ 200

Question 9: Identify and correct the mistake: The statement 'x ≥ 3 and x ≤ 1' is true for any x.

Answer: Incorrect, because x cannot be both ≥ 3 and ≤ 1 at the same time. The correct statement is 'x ≥ 3 or x ≤ 1'.

Question 10: Compare: Is 7 ≥ 7? Explain with reasoning.

Answer: Yes, because 7 ≥ 7 is true; they are equal.

Question 11: Challenge: Find a pair of numbers where one is strictly greater than the other, but also satisfies the inequality: number1 ≥ number2.

Answer: Example: 5 ≥ 3 (true).