Bluebook SAT Test Linear Inequalities in One or Two Variables 5 — Questions and Answers
Question 1: If 5 − 3x ≤ −4, which of the following MUST be true?
- x ≤ 3
- x ≥ 3 (Correct answer)
- x ≤ −3
- x ≥ −3
Correct answer: x ≥ 3
−3x ≤ −9 → x ≥ 3.
Question 2: A phone plan offers unlimited texts for $25/month or $0.05 per text. For how many texts does the unlimited plan become less expensive?
- More than 400 texts
- More than 500 texts (Correct answer)
- More than 250 texts
- More than 350 texts
Correct answer: More than 500 texts
0.05t > 25 → t > 500.
Question 3: What is the greatest integer that satisfies 4x + 9 < 25?
- 3 (Correct answer)
- 4
- 5
- 6
Correct answer: 3
4x < 16 → x < 4; the greatest integer strictly less than 4 is 3.
Question 4: Which inequality is equivalent to 3 − 4x ≥ 11?
- x ≥ −2
- x ≤ −2 (Correct answer)
- x ≥ 2
- x ≤ 2
Correct answer: x ≤ −2
−4x ≥ 8 → x ≤ −2.
Question 5: A swim team needs at least 8 members. It currently has 5. Which inequality shows additional members n needed?
- 5 + n > 8
- 5 + n < 8
- 5 + n ≥ 8 (Correct answer)
- 5 + n ≤ 8
Correct answer: 5 + n ≥ 8
5 + n ≥ 8.
Question 6: Solve: −5 ≤ 2x + 3 ≤ 9
- −4 ≤ x ≤ 3 (Correct answer)
- −1 ≤ x ≤ 6
- −4 ≤ x ≤ 6
- −1 ≤ x ≤ 3
Correct answer: −4 ≤ x ≤ 3
Subtract 3: −8 ≤ 2x ≤ 6; divide by 2: −4 ≤ x ≤ 3.
Question 7: If 3a > 15 and 2b < 8, which of the following must be true?
- a + b > 9
- a − b > 1
- a > b (Correct answer)
- ab > 20
Correct answer: a > b
a > 5 and b < 4, so a > b is always true.
Bluebook SAT Test Linear Inequalities in One or Two Variables 5
If 5 − 3x ≤ −4, which of the following MUST be true?