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

Answer: Open circle at 3, shading to the right

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

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

Question 3: Plot the solution to 4 ≤ x < 7 on the number line.

Answer: Closed circle at 4, open circle at 7, shading between

Question 4: Plot the solution set of x ≠ 0 on the number line.

Answer: Open circle at 0, shading both sides, excluding 0

Question 1: Given that x > 2 and x < 6, represent the solution set on a number line and explain your reasoning.

Answer: Open circle at 2, open circle at 6, shading in between, because x is greater than 2 and less than 6.

Question 2: If x ≤ -1 or x ≥ 4, draw and describe the solution set on the number line.

Answer: Closed circle at -1 shading left, and closed circle at 4 shading right, with two disjoint shaded regions.

Question 3: Solve the inequality 3x - 2 ≤ 7 and represent the solution on a number line.

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

Question 4: Determine the set of x satisfying -4 < x + 1 ≤ 2 and show this on the number line.

Answer: x > -5 and x ≤ 1, open circle at -5, closed circle at 1, shading in between

Question 5: Explain how you would represent the inequality x ≠ 3 on a number line.

Answer: Plot an open circle at 3 and shade all points except at 3, indicating x can be any value except 3.

Question 1: A bus fare is free for children aged less than 12. Represent this age restriction on a number line.

Answer: Open circle at 12, shading to the left, indicating ages less than 12

Question 2: A factory produces items with a maximum weight limit of 50 kg. Show this limit on a number line.

Answer: Closed circle at 50, shading to the left, representing weights up to and including 50kg

Question 1: Solve for x in the compound inequality: 1 < 2x + 3 < 7, and illustrate the solution on the number line.

Answer: x > -1 and x < 2, plot open circles at -1 and 2, shading between

Question 2: Construct and describe the set of solutions for the inequality |x - 4| > 2 on the number line.

Answer: x < 2 or x > 6, with open circles at 2 and 6, shading to the left of 2 and right of 6

Question 1: Plot the solution for x ≥ -3 and x < 2 on the number line.

Answer: Closed circle at -3 shading right, open circle at 2 shading left

Question 2: Represent the inequality x ≠ 5 on a number line.

Answer: Open circle at 5, shading both sides, excluding 5

Question 1: A student plots x > 4 as a closed circle at 4 shading to the right. Is this correct? Explain and correct if necessary.

Answer: No, it should be an open circle because x > 4 does not include 4; correct by drawing an open circle at 4 and shading right.

Question 2: A student represents x ≤ -2 with an open circle. Is this correct? Why or why not?

Answer: No, it should be a closed circle because x ≤ -2 includes -2; correction: draw a closed circle at -2.