Bluebook SAT Test Linear Inequalities in One or Two Variables 7 — Questions and Answers
Question 1: Which of the following is in the solution set of both x > −2 and x ≤ 5?
- x = −3
- x = 6
- x = 0 (Correct answer)
- x = 5.5
Correct answer: x = 0
Need −2 < x ≤ 5; x = 0 satisfies both.
Question 2: Solve for x: 5x − 8 < 3x + 4
- x < 2
- x < 4
- x < 6 (Correct answer)
- x < 12
Correct answer: x < 6
2x < 12 → x < 6.
Question 3: A taxi driver wants to earn more than $120 in a shift at $3 per mile. He has driven 20 miles. How many more miles m must he drive?
- m > 20 (Correct answer)
- m ≥ 20
- m > 40
- m ≥ 40
Correct answer: m > 20
3(20 + m) > 120 → 60 + 3m > 120 → 3m > 60 → m > 20.
Question 4: If −3 ≤ x ≤ 5, what is the greatest possible value of 2x − 1?
- 7
- 9 (Correct answer)
- 10
- 11
Correct answer: 9
Maximize by choosing x = 5: 2(5) − 1 = 9.
Question 5: Which point is in the region defined by y > 2x − 3 AND y < −x + 6?
- (0, −4)
- (4, 4)
- (1, 2) (Correct answer)
- (3, 0)
Correct answer: (1, 2)
Test (1, 2): 2 > −1 ✓; 2 < 5 ✓.
Question 6: Solve for n: 3n + 4 > −8 AND 2n − 1 ≤ 5
- −4 < n ≤ 3
- n > −4 and n ≤ 3
- −4 ≤ n ≤ 3
- Both A and B express the same solution (Correct answer)
Correct answer: Both A and B express the same solution
n > −4 and n ≤ 3; options A and B state the same solution in different notation.
Question 7: Which value of t satisfies 2t + 1 ≥ 7 but NOT t − 3 > 4?
- t = 2
- t = 3 (Correct answer)
- t = 8
- t = 9
Correct answer: t = 3
2t ≥ 6 → t ≥ 3; t > 7 excluded; t = 3 satisfies t ≥ 3 and not t > 7.
Bluebook SAT Test Linear Inequalities in One or Two Variables 7
Which of the following is in the solution set of both x > −2 and x ≤ 5?