Question 1: Plot the inequality y ≤ 3 on the number line.

Answer: Student plots the line at 3 with shading to the left

Question 2: Solve for x: x > -2. Show the number line representation.

Answer: Student indicates open circle at -2 and shading to the right

Question 3: Construct a number line to show the solution set of y ≥ 1.5.

Answer: Shaded area at 1.5 with closed circle, shading to the right

Question 4: A sound level must be less than 85 decibels for safe listening. Write the inequality and plot it.

Answer: Sound level < 85; plot with open circle at 85 and shading to the left

Question 5: On the number line, represent the inequality 2x + 1 ≤ 7.

Answer: x ≤ 3, plot at 3 with shading to the left

Question 6: A microphone detects sound levels between -10 dB and 20 dB. Write these as inequalities and plot on the number line.

Answer: -10 ≤ sound level ≤ 20; plot with closed circles at -10 and 20, shading in between

Question 7: A musician's volume setting must be greater than or equal to 5 and less than 10. Write and plot this.

Answer: volume ≥ 5 and < 10; plot with closed circle at 5 (shading right), open circle at 10 (shading left)

Question 8: Identify the mistake in this plotting: plotting y ≥ 4 with an open circle.

Answer: Incorrect; for y ≥ 4, the circle should be closed because the inequality includes 4

Question 9: Solve for x: -3x > 9 and plot the solution.

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

Question 10: The sound level is recorded as greater than 60 dB. Write and represent this inequality on a number line.

Answer: sound level > 60; open circle at 60, shading right

Question 11: Challenge: The inequality 3x - 2 ≤ 4x + 1 describes sound volume levels. Solve for x and plot the solution.

Answer: x ≥ -3; plot at -3 with shading to the right