Question 1: Simplify and write the solution set for: 3x + 5 ≥ 11.

Answer: x ≥ 2

Question 2: Solve for y: 2y ≤ 8.

Answer: y ≤ 4

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

Answer:

Question 4: Construct a triangle with sides of lengths 5, 7, and 9 units, such that the inequality involving the largest side is satisfied. (Hint: Check the triangle inequality involving ≥ or ≤)

Answer:

Question 5: Determine whether the statement 4x - 3 ≤ 1 is true for x = 1.5. Show your working.

Answer: Yes, because 4(1.5) - 3 = 6 - 3 = 3, and 3 ≤ 1 is false; so x=1.5 does not satisfy the inequality.

Question 6: A car's speed v km/h is at least 60 km/h but no more than 100 km/h. Write this as an inequality.

Answer: 60 ≤ v ≤ 100

Question 7: A box contains numbers. The smallest number is at most 5, and the largest number is at least 10. Express this as inequalities.

Answer: smallest ≤ 5 and largest ≥ 10

Question 8: Identify and correct the mistake in this statement: 'x ≥ 4 means x is less than 4.'

Answer: Corrected: x ≥ 4 means x is greater than or equal to 4.

Question 9: Solve the inequality: 2(3x - 4) ≥ 10.

Answer: x ≥ 4

Question 10: A student scores at least 70 marks in an exam but no more than 85. Write an inequality to represent this.

Answer: 70 ≤ score ≤ 85

Question 11: Challenge: The temperature T in degrees Celsius is at least -5°C but not more than 3°C. Express this as an inequality.

Answer: -5 ≤ T ≤ 3

Question 12: Identify the common mistake in the statement: 'If x ≥ 3, then x is less than 3.'

Answer: Mistake: x ≥ 3 means x is greater than or equal to 3, not less.