Bluebook SAT Test Linear Inequalities in One or Two Variables 3 — Questions and Answers
Question 1: Which of the following is a solution to −4x + 3 ≥ 11?
- x = 0
- x = −1
- x = −3 (Correct answer)
- x = 1
Correct answer: x = −3
−4x ≥ 8 → x ≤ −2; only x = −3 satisfies x ≤ −2.
Question 2: Solve for x: (x − 1)/2 < 4
- x < 5
- x < 7
- x < 9 (Correct answer)
- x < 3
Correct answer: x < 9
Multiply both sides by 2: x − 1 < 8; add 1: x < 9.
Question 3: Quality control requires a component to be between 4.95 cm and 5.05 cm, inclusive. Which inequality models acceptable length L?
- L < 4.95 or L > 5.05
- 4.95 < L < 5.05
- 4.95 ≤ L ≤ 5.05 (Correct answer)
- L = 5.00
Correct answer: 4.95 ≤ L ≤ 5.05
'Between ... inclusive' means both endpoints are included: 4.95 ≤ L ≤ 5.05.
Question 4: Which point is in the solution set of y < 2x + 1?
- (0, 2)
- (1, 3)
- (2, 4) (Correct answer)
- (−1, −1)
Correct answer: (2, 4)
Test (2, 4): 4 < 2(2)+1 = 5. True.
Question 5: Solve: −2 < 3x − 5 ≤ 7
- 1 < x ≤ 4 (Correct answer)
- 1 ≤ x < 4
- −1 < x ≤ 4
- 1 < x < 4
Correct answer: 1 < x ≤ 4
Add 5 to all parts: 3 < 3x ≤ 12; divide by 3: 1 < x ≤ 4.
Question 6: A school bus holds at most 52 students. There are already 34 on board. Which inequality shows the number of additional students s that can board?
- s > 18
- s ≥ 18
- s ≤ 18 (Correct answer)
- s < 18
Correct answer: s ≤ 18
34 + s ≤ 52 → s ≤ 18.
Question 7: For which integer value of k is 5 ≤ 2k + 1 < 13 satisfied?
- k = 1
- k = 2 (Correct answer)
- k = 6
- k = 7
Correct answer: k = 2
Subtract 1: 4 ≤ 2k < 12; divide by 2: 2 ≤ k < 6; integers are 2, 3, 4, 5; k = 2 is the first listed.
Bluebook SAT Test Linear Inequalities in One or Two Variables 3
Which of the following is a solution to −4x + 3 ≥ 11?