Question 1: Solve for x: 3x + 5 > 11.

Answer: x > 2

Question 2: Solve for x: 2( x - 4 ) ≤ 10.

Answer: x ≤ 9

Question 3: Simplify and solve: 5 - 2x < 1.

Answer: x > 2

Question 4: Plot the graph of y = 2x on the grid. (Draw the line and shade the region y > 2x).

Answer: Line y=2x; region above the line shaded.

Question 5: Construct a triangle with sides of length 5, 7, and 9 units. Ensure the shape is possible and label the sides.

Answer: Valid triangle; sum of any two sides > third side.

Question 6: Solve the inequality: -4x + 3 ≤ 11.

Answer: x ≥ -2

Question 7: A store offers a discount such that the total price p (in dollars) after discount satisfies p < 50. If the original price is x dollars and the discount is 20% of x, write an inequality and solve for x.

Answer: 0.8x < 50; x < 62.5

Question 8: Identify and correct the mistake in solving: 2x - 3 > 7 ⇒ 2x > 4 ⇒ x > 2.

Answer: Incorrect step: 2x - 3 > 7; add 3 to both sides: 2x > 10; then divide both sides by 2: x > 5. The correct solution is x > 5.

Question 9: Solve for x: 4( x + 2 ) ≥ 20.

Answer: x ≥ 3

Question 10: A car rental company has a policy: total cost c (in dollars) is less than or equal to $300 if the number of days d is less than or equal to 5, with a daily rate of $50 plus a fixed fee of $50. Set up and solve the inequality for d.

Answer: 50d + 50 ≤ 300; 50d ≤ 250; d ≤ 5

Question 11: Solve for x: - (x - 3) > 4.

Answer: x < -1