Question 1: Solve for x: 3x - 5 > 7

Answer: x > 4

Question 2: Solve the inequality: 2( x + 4 ) ≤ 10

Answer: x ≤ 1

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

Answer: x > 2

Question 4: Plot the graph of y > 2x + 3 on the grid provided.

Answer: See full answer key

Question 5: Construct a triangle with sides that satisfy the inequality: x + 2 < 7 (where x represents the length of one side).

Answer: See full answer key

Question 6: Solve for x: -4x + 6 ≥ 2x + 8

Answer: x ≤ -1

Question 7: A student scores at least 85 in a test to pass. Write an inequality for the test score, x.

Answer: x ≥ 85

Question 8: Solve: 3( x - 2 ) > 4x + 1

Answer: x < -7

Question 9: A bakery offers a discount such that the price p after discount satisfies p < 50. If the original price is $p, write the inequality and explain what it means.

Answer: p < 50; the discounted price is less than $50

Question 10: Identify and correct the mistake in solving: 2x + 3 < 7, student writes x < 2.

Answer: Incorrect; the correct solution is x < 2, so the student's answer is correct. But if the student wrote x > 2, then correction needed.

Question 11: Solve: x/3 + 2 ≤ 4

Answer: x ≤ 6

Question 12: Challenge: Find all x that satisfy the inequality: 4x - 5 < 3x + 2 and explain your reasoning.

Answer: x < 7; subtract 3x from both sides, add 5 to both sides, then solve for x.