Question 1: Simplify and write the inequality: 3x + 5 ≥ 11.

Answer: x ≥ 2

Question 2: Solve for y: 2y - 4 ≤ 10.

Answer: y ≤ 7

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

Answer:

Question 4: Construct a triangle with side lengths that satisfy the inequality: side1 + side2 ≥ side3.

Answer:

Question 5: If 5a + 3 ≥ 23, what is the smallest integer value of a?

Answer: a ≥ 4.6 (so a ≥ 5)

Question 6: Write an inequality to represent: 'A number n is at least 15.'

Answer: n ≥ 15

Question 7: Determine if the statement is true or false: 7 ≥ 5 + 2.

Answer: True

Question 8: A student scores 78 or more in a test to pass: write the inequality. How many scores qualify?

Answer: score ≥ 78; scores ≥ 78 qualify

Question 9: Challenge: Find all x such that 4x - 1 ≤ 3x + 7.

Answer: x ≤ 8

Question 10: A rectangle has a length at least 12 units and width no more than 5 units. Write inequalities to express these conditions.

Answer: length ≥ 12; width ≤ 5

Question 11: Error analysis: Identify the mistake in the statement: 'x + 2 ≥ 5' implies x ≥ 3, but the student says x ≥ 2.

Answer: Incorrect; x ≥ 3, not x ≥ 2