Bluebook SAT Test Linear Inequalities in One or Two Variables 10 — Questions and Answers
Question 1: If 4 ≤ 3x − 2 ≤ 13, what is one possible integer value of x?
- 3 (Correct answer)
- 7
- 0
- −1
Correct answer: 3
Adding 2: 6 ≤ 3x ≤ 15 → 2 ≤ x ≤ 5; integers in this range include 2, 3, 4, 5. x = 3 qualifies.
Question 2: Which graph represents the solution of 2 − x > −3 on a number line?
- Open circle at 5, shaded to the left (Correct answer)
- Closed circle at 5, shaded to the left
- Open circle at −5, shaded to the right
- Closed circle at −5, shaded to the right
Correct answer: Open circle at 5, shaded to the left
2 − x > −3 → −x > −5 → x < 5; plotted as an open circle at 5 with shading left.
Question 3: A gardener needs to fence a rectangular area with at most 80 feet of fencing. The width is fixed at 15 feet. Which inequality represents possible lengths L?
- 2L + 30 ≤ 80 (Correct answer)
- 2L + 15 ≤ 80
- L + 30 ≤ 80
- L + 15 ≤ 80
Correct answer: 2L + 30 ≤ 80
Perimeter = 2L + 2(15) = 2L + 30; this must be ≤ 80, giving 2L + 30 ≤ 80.
Question 4: Which value of k makes the inequality 2k − 9 > k + 1 true?
- 11 (Correct answer)
- 10
- 9
- 5
Correct answer: 11
2k − 9 > k + 1 → k > 10; only k = 11 satisfies this.
Question 5: How many positive integers satisfy 3x + 5 < 20?
- 4 (Correct answer)
- 5
- 3
- 6
Correct answer: 4
3x < 15 → x < 5; positive integers less than 5 are 1, 2, 3, 4 — exactly 4 values.
Question 6: Which point is NOT in the solution region of y ≥ −x + 4?
- (0, 3) (Correct answer)
- (2, 2)
- (5, 0)
- (−1, 6)
Correct answer: (0, 3)
At (0, 3): y = 3 and −x + 4 = 4; since 3 < 4, the point is below the line and not in the solution region.
Question 7: Solve: −(x + 4) ≥ 2x − 1
- x ≤ −1 (Correct answer)
- x ≥ −1
- x ≤ 1
- x ≥ 1
Correct answer: x ≤ −1
Expanding: −x − 4 ≥ 2x − 1 → −3x ≥ 3 → x ≤ −1.
Question 8: A student needs to average at least 80 on three tests. The first two scores are 74 and 85. What is the minimum score s needed on the third test?
- 81 (Correct answer)
- 80
- 79
- 78
Correct answer: 81
(74 + 85 + s)/3 ≥ 80 → 159 + s ≥ 240 → s ≥ 81.
Bluebook SAT Test Linear Inequalities in One or Two Variables 10
If 4 ≤ 3x − 2 ≤ 13, what is one possible integer value of x?