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Absolute value equations and inequalities

12th grade (Year 13 in England) · 16 questions · Common Core: HSA.REI.B.3, HSA.CED.A.1

Name

Date

Score/ 16

  1. Question 1

    Solve: |x − 4| = 1. Give both solutions, separated by a comma.

    x =

  2. Question 2

    Solve: |x + 4| > 1

    • A. x < −5 or x > −3
    • B. −5 < x < −3
    • C. x < −3
    • D. 3 < x < 5

  3. Question 3

    Solve: |2x + 12| = 6. Give both solutions, separated by a comma.

    x =

  4. Question 4

    Solve: |x − 4| > 6

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

  5. Question 5

    Solve: |2x + 4| = 8. Give both solutions, separated by a comma.

    x =

  6. Question 6

    Solve: |x − 6| < 4

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

  7. Question 7

    Solve: |2x + 8| = 10. Give both solutions, separated by a comma.

    x =

  8. Question 8

    Solve: |x − 3| > 3

    • A. x < 0 or x > 6
    • B. x < 6
    • C. −6 < x < 0
    • D. 0 < x < 6

  9. Question 9

    Solve: |3x − 9| = 6. Give both solutions, separated by a comma.

    x =

  10. Question 10

    Solve: |x − 5| > 3

    • A. x < 2 or x > 8
    • B. −8 < x < −2
    • C. 2 < x < 8
    • D. x < 8

  11. Question 11

    Solve: |3x − 3| = 3. Give both solutions, separated by a comma.

    x =

  12. Question 12

    Solve: |x − 1| < 4

    • A. −3 < x < 5
    • B. x < 5
    • C. x < −3 or x > 5
    • D. −5 < x < 3

  13. Question 13

    Solve: |2x + 8| = 2. Give both solutions, separated by a comma.

    x =

  14. Question 14

    Solve: |x − 4| > 8

    • A. −12 < x < 4
    • B. −4 < x < 12
    • C. x < 12
    • D. x < −4 or x > 12

  15. Question 15

    Solve: |3x + 21| = 3. Give both solutions, separated by a comma.

    x =

  16. Question 16

    Solve: |x| < 2

    • A. −2 < x < 2
    • B. x < 2
    • C. x < −2 or x > 2

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