Bluebook SAT Test Linear Inequalities in One or Two Variables 9 — Questions and Answers
Question 1: If 7 − 3x ≥ −2, which of the following is the solution set?
- x ≤ 3 (Correct answer)
- x ≥ 3
- x ≤ −3
- x ≥ −3
Correct answer: x ≤ 3
Subtracting 7 gives −3x ≥ −9, and dividing by −3 (flipping the sign) gives x ≤ 3.
Question 2: A theater sells adult tickets for $12 and student tickets for $8. The drama club needs to raise at least $240. If they sell exactly 10 adult tickets, what is the minimum number of student tickets s they must sell?
- 15 (Correct answer)
- 18
- 12
- 20
Correct answer: 15
10(12) + 8s ≥ 240 → 120 + 8s ≥ 240 → 8s ≥ 120 → s ≥ 15.
Question 3: Which of the following is a solution to the inequality −5x + 2 > 17?
- x = −4 (Correct answer)
- x = −2
- x = 0
- x = 3
Correct answer: x = −4
−5(−4) + 2 = 22 > 17 ✓; for all other choices the inequality fails.
Question 4: On a number line, the inequality −4 < 2x ≤ 8 is represented by what interval?
- (−2, 4] (Correct answer)
- [−2, 4)
- (−4, 8]
- [−4, 8)
Correct answer: (−2, 4]
Dividing every part by 2 gives −2 < x ≤ 4, which corresponds to the interval (−2, 4].
Question 5: Alicia wants to keep her monthly phone bill under $60. Her plan charges $20 plus $0.08 per text. Which inequality gives the maximum number of texts t she can send?
- 0.08t < 40 (Correct answer)
- 0.08t ≤ 40
- 0.08t > 40
- 0.08t ≥ 40
Correct answer: 0.08t < 40
20 + 0.08t < 60 simplifies to 0.08t < 40, so t < 500.
Question 6: Which ordered pair satisfies the inequality 3x − 2y > 6?
- (4, 2) (Correct answer)
- (1, 0)
- (2, 1)
- (0, −3)
Correct answer: (4, 2)
3(4) − 2(2) = 8 > 6 ✓; the other choices yield 3, 3, and 6, which do not satisfy the strict inequality.
Question 7: Solve for x: (2x + 1)/3 < 5
- x < 7 (Correct answer)
- x > 7
- x < 14
- x > 14
Correct answer: x < 7
Multiply both sides by 3: 2x + 1 < 15 → 2x < 14 → x < 7.
Question 8: A warehouse can hold at most 500 boxes. There are already 185 boxes inside. A forklift loads b boxes at a time and makes at least 5 trips. Which inequality correctly models this situation?
- 185 + 5b ≤ 500 (Correct answer)
- 5b ≤ 500
- 185 + 5b ≥ 500
- 5b ≥ 500
Correct answer: 185 + 5b ≤ 500
After 5 trips, the total is 185 + 5b, and this must not exceed 500, giving 185 + 5b ≤ 500.
Bluebook SAT Test Linear Inequalities in One or Two Variables 9
If 7 − 3x ≥ −2, which of the following is the solution set?