Bluebook SAT Test Linear Inequalities in One or Two Variables 2 — Questions and Answers
Question 1: Solve for x: −3x + 6 > 15
- x > 3
- x < 3
- x > −3
- x < −3 (Correct answer)
Correct answer: x < −3
−3x > 9 → x < −3 (flip when dividing by −3).
Question 2: What is the graph of 2x + 1 < 7 on a number line?
- Closed circle at 3, arrow right
- Open circle at 3, arrow left (Correct answer)
- Closed circle at 3, arrow left
- Open circle at 3, arrow right
Correct answer: Open circle at 3, arrow left
2x < 6 → x < 3; strict inequality uses open circle, arrow pointing left.
Question 3: Jacob can spend no more than $50. He picks up one book at $14. Each additional book costs $9. What is the maximum number of additional books he can buy?
- 3
- 4 (Correct answer)
- 5
- 6
Correct answer: 4
14 + 9b ≤ 50 → 9b ≤ 36 → b ≤ 4.
Question 4: Solve: 4 < 2x + 2 ≤ 12
- 1 < x ≤ 5 (Correct answer)
- 2 < x ≤ 6
- 1 ≤ x < 5
- 2 ≤ x < 6
Correct answer: 1 < x ≤ 5
Subtract 2 from all parts: 2 < 2x ≤ 10; divide by 2: 1 < x ≤ 5.
Question 5: The sum of a number and 6 is at most 10. Which inequality represents this?
- n + 6 < 10
- n + 6 ≤ 10 (Correct answer)
- n + 6 ≥ 10
- n + 6 > 10
Correct answer: n + 6 ≤ 10
'At most 10' means ≤ 10, so n + 6 ≤ 10.
Question 6: Which value of y does NOT satisfy 3y − 2 < 10?
- y = 0
- y = 2
- y = 3
- y = 4 (Correct answer)
Correct answer: y = 4
3y < 12 → y < 4; y = 4 does not satisfy y < 4.
Question 7: At a carnival, rides cost $2.50 each and food costs $8. Leila has $28. After buying food, how many rides can she go on at most?
- 6
- 7
- 8 (Correct answer)
- 9
Correct answer: 8
8 + 2.50r ≤ 28 → 2.50r ≤ 20 → r ≤ 8.
Bluebook SAT Test Linear Inequalities in One or Two Variables 2
Solve for x: −3x + 6 > 15