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Solve double inequalities like a < bx + c < d

9th grade (Year 10 in England) · 16 questions · Common Core: HSA.REI.B.3 · England: GCSE Higher Algebra

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1
Question 1
Solve: 3x + 4 > 7 and 3x + 4 ≤ 10. Write the answer as one double inequality.
- A. 1 ≤ x ≤ 2
- B. x ≤ 1 or x ≥ 2
- C. 1 ≤ x < 2
- D. 1 < x ≤ 2
2
Question 2
Solve: −12 < 4x + 4 < −4
- A. −16 < x < −8
- B. 0 < x < 2
- C. −4 > x > −2
- D. −4 < x < −2
3
Question 3
Solve: −14 < −4x − 6 < 6
- A. −3 < x < 2
- B. −8 < x < 12
- C. −2 < x < 3
- D. 2 < x < −3
4
Question 4
Solve: 2x + 3 ≥ −1 and 2x + 3 < 1. Write the answer as one double inequality.
- A. −2 ≤ x < −1
- B. −2 ≤ x ≤ −1
- C. x ≤ −2 or x ≥ −1
- D. −2 < x ≤ −1
5
Question 5
Solve: −15 < 4x + 1 < 13
- A. −4 < x < 3
- B. −16 < x < 12
- C. −4 > x > 3
- D. −3 < x < 4
6
Question 6
Solve: −3 < −x − 1 < 2
- A. −3 < x < 2
- B. −2 < x < 3
- C. 2 < x < −3
7
Question 7
Solve: 4x + 2 ≥ 2 and 4x + 2 < 18. Write the answer as one double inequality.
- A. 0 < x ≤ 4
- B. 0 ≤ x ≤ 4
- C. x ≤ 0 or x ≥ 4
- D. 0 ≤ x < 4
8
Question 8
Solve: −5 < 5x + 5 < 5
- A. 3 < x < 5
- B. −2 < x < 0
- C. −2 > x > 0
- D. −3 < x < 1
9
Question 9
Solve: −22 < −4x + 2 < −6
- A. 6 < x < 2
- B. −24 < x < −8
- C. −6 < x < −2
- D. 2 < x < 6
10
Question 10
Solve: 4x + 1 > −11 and 4x + 1 ≤ −3. Write the answer as one double inequality.
- A. −3 ≤ x < −1
- B. x ≤ −3 or x ≥ −1
- C. −3 ≤ x ≤ −1
- D. −3 < x ≤ −1
11
Question 11
Solve: −7 < 4x + 5 < 5
- A. 2 < x < 5
- B. −12 < x < 0
- C. −3 < x < 0
- D. −3 > x > 0
12
Question 12
Solve: −5 < −x + 2 < 0
- A. 7 < x < 2
- B. −7 < x < −2
- C. 2 < x < 7
13
Question 13
Solve: 2x + 4 > −4 and 2x + 4 ≤ 4. Write the answer as one double inequality.
- A. −4 ≤ x ≤ 0
- B. x ≤ −4 or x ≥ 0
- C. −4 ≤ x < 0
- D. −4 < x ≤ 0
14
Question 14
Solve: −17 < 3x + 1 < −5
- A. −6 > x > −2
- B. −6 < x < −2
- C. −18 < x < −6
- D. −7 < x < −1
15
Question 15
Solve: −11 < −4x + 5 < −3
- A. 4 < x < 2
- B. −16 < x < −8
- C. −4 < x < −2
- D. 2 < x < 4
16
Question 16
Solve: 3x + 5 > 11 and 3x + 5 ≤ 26. Write the answer as one double inequality.
- A. 2 ≤ x < 7
- B. 2 < x ≤ 7
- C. x ≤ 2 or x ≥ 7
- D. 2 ≤ x ≤ 7

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Answer key: Solve double inequalities like a < bx + c < d

1. D. 1 < x ≤ 2
2. D. −4 < x < −2
3. A. −3 < x < 2
4. A. −2 ≤ x < −1
5. A. −4 < x < 3
6. A. −3 < x < 2
7. D. 0 ≤ x < 4
8. B. −2 < x < 0
9. D. 2 < x < 6
10. D. −3 < x ≤ −1
11. C. −3 < x < 0
12. C. 2 < x < 7
13. D. −4 < x ≤ 0
14. B. −6 < x < −2
15. D. 2 < x < 4
16. B. 2 < x ≤ 7