Bluebook SAT Test Linear Inequalities in One or Two Variables 8 — Questions and Answers
Question 1: If 4 − x > 1, which of the following is a possible value of x?
- x = 3
- x = 4
- x = 2 (Correct answer)
- x = 5
Correct answer: x = 2
−x > −3 → x < 3; only x = 2 satisfies x < 3.
Question 2: Solve: 3 ≤ 5 − x < 8
- −3 < x ≤ 2 (Correct answer)
- −3 ≤ x < 2
- 3 < x ≤ 8
- −2 < x ≤ 3
Correct answer: −3 < x ≤ 2
Subtract 5: −2 ≤ −x < 3; multiply by −1 (flip both): −3 < x ≤ 2.
Question 3: A runner burns 10 calories per minute and wants to burn more than 350 calories. Which inequality shows the minimum time t needed?
- 10t < 350
- 10t ≤ 350
- 10t > 350 (Correct answer)
- 10t ≥ 350
Correct answer: 10t > 350
'More than 350' is a strict inequality: 10t > 350.
Question 4: For which integer values of x is both 2x > −6 and 3x ≤ 9 satisfied?
- x = −4, −3
- x = −2, −1, 0, 1, 2, 3 (Correct answer)
- x = 0, 1, 2, 3 only
- x = 4, 5, 6
Correct answer: x = −2, −1, 0, 1, 2, 3
x > −3 and x ≤ 3; integers: −2, −1, 0, 1, 2, 3.
Question 5: Which system of inequalities is satisfied by the point (2, 5)?
- y > 3x and y < x + 2
- y < 3x and y > x + 2
- y ≤ 3x and y ≥ x + 2 (Correct answer)
- y ≥ 3x and y ≤ x + 2
Correct answer: y ≤ 3x and y ≥ x + 2
Test (2, 5) in C: 5 ≤ 6 ✓; 5 ≥ 4 ✓.
Question 6: The difference of two numbers is at least 7. The smaller number is 3. What is the minimum value of the larger number?
- 4
- 7
- 10 (Correct answer)
- 21
Correct answer: 10
L − 3 ≥ 7 → L ≥ 10; minimum is 10.
Question 7: For what values of x is 3x − 2 strictly between 4 and 16?
- 1 < x < 5
- 2 < x < 6 (Correct answer)
- 1 ≤ x ≤ 5
- 2 ≤ x ≤ 6
Correct answer: 2 < x < 6
4 < 3x − 2 < 16 → 6 < 3x < 18 → 2 < x < 6.
Bluebook SAT Test Linear Inequalities in One or Two Variables 8
If 4 − x > 1, which of the following is a possible value of x?