Question 1: Solve for x: 3x - 5 > 10.

Answer: x > 5

Question 2: Solve for y: -2y + 4 ≤ 0.

Answer: y ≥ 2

Question 3: Solve: 5(2x - 3) < 20.

Answer: x < 4

Question 4: Solve for z: 4z + 1 ≥ 3z + 2.

Answer: z ≥ 1

Question 1: Solve the inequality: 2(3x - 4) + 5 < 3(x + 2). Show all steps.

Answer: x < 2

Question 2: A school fundraiser requires that the number of tickets sold, t, satisfies the inequality t ≥ 50 and t ≤ 200. If the number of tickets sold is represented by the inequality 3t + 20 ≥ 170, determine if the sale goal is met. Explain your reasoning.

Answer: Yes, because t ≥ 50 and t ≤ 200, and solving 3t + 20 ≥ 170 gives t ≥ 50, so the goal is met.

Question 1: A mobile data plan costs £10 plus £0.05 per MB used. The maximum budget is £25. Write and solve an inequality to find the maximum number of MBs that can be used without exceeding the budget.

Answer: 0.05x + 10 ≤ 25, so x ≤ 300 MB

Question 1: Solve the inequality: 2(3x - 2) - (x + 4) > 3(x - 1). Show your detailed working.

Answer: x > 2

Question 2: Construct and solve an inequality representing the scenario: 'A company can only produce between 100 and 500 units per week. If production p is modeled by p ≥ 20x - 50, find the range of x that satisfies the production constraints.'

Answer: x ≥ 7.5 and x ≤ 27.5

Question 1: Error analysis: A student solves 4x - 3 > 5 and writes the solution as x > 2. Explain what mistake was made and correct the solution.

Answer: They forgot to divide both sides by 4; correct solution: x > 2

Question 2: Another student solves -2x + 4 ≤ 0 and writes x ≤ 2. Identify the error and give the correct solution.

Answer: They did not divide both sides by -2; correct solution: x ≥ 2