Question 1: Solve for x: 3x - 5 > 4

Answer: 3

Question 2: Solve the inequality: 2x + 3 ≤ 7

Answer: 2

Question 3: Solve for x: -4x + 6 < 14

Answer: -2

Question 4: Plot the graph of y > 2x - 1 on the grid.

Answer: Student plots the boundary line y=2x-1 and shades above.

Question 5: Construct a triangle on the grid where the sides satisfy the inequality: x + y < 6.

Answer: Student draws a triangle with points satisfying x + y < 6.

Question 1: Solve the inequality: 5x - 2 ≤ 3x + 4.

Answer: 3

Question 2: Solve for x: -2(3x - 1) > 4x + 5.

Answer: -1

Question 3: Solve the inequality: 7 - 2x ≥ 1.

Answer: 3

Question 4: Plot the graph of y < -x + 4 on the grid.

Answer: Student shades below the boundary line y=−x+4.

Question 1: A school bus can carry at most 50 students. If x students are on the bus and 10 more join, write an inequality to represent the situation. Solve for x.

Answer: x + 10 ≤ 50; x ≤ 40

Question 2: A factory produces a maximum of 200 units per day. If y units are produced today, and tomorrow 30 more units are produced, write and solve an inequality to find the maximum y.

Answer: y + 30 ≤ 200; y ≤ 170

Question 1: A mobile phone plan costs a maximum of £30 per month. Calls cost 10p per minute. Write an inequality to determine the maximum number of minutes you can talk without exceeding £30.

Answer: 0.10m ≤ 30; m ≤ 300

Question 1: Solve for x: 2(3x - 4) > x + 10, then interpret the solution in words.

Answer: x > 6; solutions where x is greater than 6.

Question 2: Construct an inequality to model the scenario: A store sells items for £5 each. The total cost should be less than or equal to £40. Find the maximum number of items.

Answer: 5n ≤ 40; n ≤ 8

Question 1: Student's solution: Solve x - 4 < 7. Student writes: x < 7 + 4, so x < 11. Is this correct? If not, correct the mistake.

Answer: Yes, x < 11 is correct.

Question 2: Solve for x: 6x + 2 > 4x + 5. Show the correct steps.

Answer: x > 1.5