Question 1: Simplify and state the inequality: 3x + 5 ≥ 14.

Answer: x ≥ 3

Question 2: Solve for y: 2y − 7 ≤ 5.

Answer: y ≤ 6

Question 3: Plot the graph of y ≥ 2x + 1 on the grid below.

Answer: Students will draw the region y ≥ 2x + 1.

Question 4: Construct a triangle with sides of lengths at least 5 cm and at most 10 cm, such that the side lengths satisfy a ≤ b ≥ c. Use the grid to draw your triangle.

Answer: Diagram demonstrating the side lengths and inequalities.

Question 5: A car's speed v must be at least 60 km/h but not more than 100 km/h. Write an inequality for v.

Answer: 60 ≤ v ≤ 100

Question 6: In a survey, the number of students who prefer chocolate ice cream is at least 30 but fewer than 50. Write the inequality representing this scenario.

Answer: 30 ≤ x < 50

Question 7: If a temperature T is greater than or equal to 15°C and less than 25°C, express this as an inequality.

Answer: 15 ≤ T < 25

Question 8: A company’s profit P is at least £50,000 but less than £200,000. Write the inequality for P.

Answer: 50,000 ≤ P < 200,000

Question 9: Calculate the smallest integer x that satisfies: x ≥ 7.5.

Answer: x ≥ 8

Question 10: Identify and correct the mistake in the statement: 'x ≥ 4 and x ≤ 2.'

Answer: The inequality x ≥ 4 and x ≤ 2 is impossible; it should be x ≥ 2 and x ≤ 4.

Question 11: A student claims that for all real x, if x ≥ 3 then x ≥ 2. Is this statement true? Justify your answer.

Answer: Yes, because if x ≥ 3, then x is certainly ≥ 2.