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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: −12 < 5x − 2 < 8

    • A. −3 < x < 3
    • B. −10 < x < 10
    • C. −2 < x < 2
    • D. −2 > x > 2

  2. Question 2

    Solve: 3x − 5 > 1 and 3x − 5 ≤ 7. Write the answer as one double inequality.

    • A. 2 ≤ x ≤ 4
    • B. 2 ≤ x < 4
    • C. 2 < x ≤ 4
    • D. x ≤ 2 or x ≥ 4

  3. Question 3

    Solve: −15 < −3x < 0

    • A. 5 < x < 0
    • B. 0 < x < 5
    • C. −15 < x < 0
    • D. −5 < x < 0

  4. Question 4

    Solve: 8 < 3x + 5 < 26

    • A. 1 < x < 7
    • B. 3 < x < 21
    • C. 1 > x > 7
    • D. 0 < x < 8

  5. Question 5

    Solve: 4x + 2 ≥ 10 and 4x + 2 < 30. Write the answer as one double inequality.

    • A. x ≤ 2 or x ≥ 7
    • B. 2 ≤ x ≤ 7
    • C. 2 ≤ x < 7
    • D. 2 < x ≤ 7

  6. Question 6

    Solve: −24 < −4x < −4

    • A. −24 < x < −4
    • B. 1 < x < 6
    • C. 6 < x < 1
    • D. −6 < x < −1

  7. Question 7

    Solve: −3 < 2x − 5 < 11

    • A. 0 < x < 9
    • B. 2 < x < 16
    • C. −4 < x < 3
    • D. 1 < x < 8

  8. Question 8

    Solve: 2x + 2 ≥ 4 and 2x + 2 < 10. Write the answer as one double inequality.

    • A. 1 < x ≤ 4
    • B. x ≤ 1 or x ≥ 4
    • C. 1 ≤ x < 4
    • D. 1 ≤ x ≤ 4

  9. Question 9

    Solve: 0 < −x + 5 < 4

    • A. −5 < x < −1
    • B. 1 < x < 5
    • C. 5 < x < 1

  10. Question 10

    Solve: −2 < 2x + 4 < 2

    • A. −3 < x < −1
    • B. −6 < x < −2
    • C. −4 < x < 0
    • D. −3 > x > −1

  11. Question 11

    Solve: 4x − 5 > −1 and 4x − 5 ≤ 7. Write the answer as one double inequality.

    • A. 1 ≤ x < 3
    • B. 1 < x ≤ 3
    • C. 1 ≤ x ≤ 3
    • D. x ≤ 1 or x ≥ 3

  12. Question 12

    Solve: 2 < −4x − 2 < 10

    • A. −1 < x < −3
    • B. 4 < x < 12
    • C. 1 < x < 3
    • D. −3 < x < −1

  13. Question 13

    Solve: 5 < 2x + 5 < 11

    • A. 0 < x < 6
    • B. −1 < x < 4
    • C. 0 < x < 3
    • D. 0 > x > 3

  14. Question 14

    Solve: 4x + 1 > −3 and 4x + 1 ≤ 9. 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

  15. Question 15

    Solve: −11 < −4x + 1 < 13

    • A. 3 < x < −3
    • B. −3 < x < 3
    • C. −12 < x < 12

  16. Question 16

    Solve: 6 < 3x < 18

    • A. 6 < x < 18
    • B. 2 < x < 6
    • C. 1 < x < 7
    • D. 2 > x > 6

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