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

Answer: Open circle at 3, shade to the right

Question 2: Identify the error in plotting the inequality x ≤ -1, where the student shaded the region to the right of -1.

Answer: Incorrect shading; should shade to the left of -1

Question 3: Solve and represent on the number line: 2x + 3 < 7.

Answer: x < 2

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

Answer: Closed circle at -2, open circle at 4, shade between

Question 5: A student plots x ≤ 5 but forgets to include the point 5 with a closed circle. Correct this mistake.

Answer: Use a closed circle at 5

Question 6: Solve the inequality: 3(2x - 1) > 4x + 5, and draw the solution on the number line.

Answer: x > 2

Question 7: A word problem: A store is open only if the temperature is above 10°C. If the temperature T is represented on the number line, which inequality represents this condition? Plot the acceptable temperatures.

Answer: T > 10, open circle at 10, shade to the right

Question 8: Construct a triangle on the grid with sides of lengths 3, 4, and 5, using the number line to verify side lengths.

Answer: Students demonstrate correct construction and use number line for side verification

Question 9: Plot the inequality: x ≤ -2 or x ≥ 3, on the same number line. Shade the regions accordingly and label them.

Answer: Closed circle at -2 shaded left; closed circle at 3 shaded right

Question 10: A student incorrectly plots x > 2.5 but shades the region to the left of 2.5. Identify and correct the mistake.

Answer: Shading should be to the right of 2.5

Question 11: Challenge: Find the set of solutions for |x - 3| < 2 and plot it on the number line.

Answer: 1 < x < 5