Question 1: Plot the solution set of x > 3 on the number line.

Answer: Open circle at 3, shading to the right

Question 2: Plot the inequality x ≤ -2 on the number line.

Answer: Closed circle at -2, shading to the left

Question 3: Solve the inequality 2x + 5 < 11 algebraically and then plot the solution.

Answer: x < 3; plot open circle at 3, shading left

Question 4: Plot the solution set of -4 ≤ 2x + 1 < 7 on the number line.

Answer: x between -0.75 and 3, closed circle at -0.75, open at 3

Question 5: A student mistakes plotting x > 2 as a closed circle at 2 and shading to the left. Explain what's wrong and correct it.

Answer: Since x > 2, the circle should be open at 2, shading to the right.

Question 6: Construct a number line to represent the solution to the inequality x ≤ -1 or x ≥ 4.

Answer: Closed circle at -1 shading left, closed circle at 4 shading right, with both regions highlighted

Question 7: Evaluate and plot the solution for 3x - 2 > 4x + 1.

Answer: x < -3; open circle at -3, shading left

Question 8: On the number line, shade the solution to the inequality 5 - 2x ≥ 1.

Answer: x ≤ 2; closed circle at 2, shading to the left

Question 9: A word problem: A store sells items costing $x$, with the budget limit at $50. Write and plot the inequality representing all affordable options.

Answer: x ≤ 50; plot closed circle at 50, shading left

Question 10: Identify and correct the mistake: Plotting x < 5 with a closed circle at 5.

Answer: The circle should be open at 5 for x < 5, not closed.

Question 11: Find the solution set for x > -2 and x ≤ 4, then plot on the number line.

Answer: x in (-2, 4]; open circle at -2, closed at 4