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Solve absolute value inequalities
11th grade (Year 12 in England) · 16 questions · Common Core: HSA.REI.B.3
Name
Date
Score/ 16
Question 1
Solve: |2x| ≤ 6
- A. −6 ≤ x ≤ 6
- B. −3 ≤ x ≤ 3
- C. x ≤ −3 or x ≥ 3
Question 2
Solve: |x + 1| < 2
- A. −3 < x < 1
- B. x < 1
- C. x ≤ −3 or x ≥ 1
- D. −1 < x < 3
Question 3
Solve: |4x + 8| ≤ 12
- A. −1 ≤ x ≤ 5
- B. −20 ≤ x ≤ 4
- C. x ≤ −5 or x ≥ 1
- D. −5 ≤ x ≤ 1
Question 4
Solve: |x − 1| ≥ 5
- A. −4 < x < 6
- B. x ≤ −4 or x ≥ 6
- C. x ≤ −6 or x ≥ 4
- D. x ≥ 6
Question 5
Solve: |2x + 6| ≤ 4
- A. 1 ≤ x ≤ 5
- B. x ≤ −5 or x ≥ −1
- C. −5 ≤ x ≤ −1
- D. −10 ≤ x ≤ −2
Question 6
Solve: |x + 3| ≥ 1
- A. x ≤ −4 or x ≥ −2
- B. −4 < x < −2
- C. x ≤ 2 or x ≥ 4
- D. x ≥ −2
Question 7
Solve: |3x − 3| ≤ 12
- A. −3 ≤ x ≤ 5
- B. x ≤ −3 or x ≥ 5
- C. −9 ≤ x ≤ 15
- D. −5 ≤ x ≤ 3
Question 8
Solve: |x + 1| < 5
- A. −4 < x < 6
- B. x ≤ −6 or x ≥ 4
- C. x < 4
- D. −6 < x < 4
Question 9
Solve: |2x − 6| ≤ 8
- A. −1 ≤ x ≤ 7
- B. x ≤ −1 or x ≥ 7
- C. −7 ≤ x ≤ 1
- D. −2 ≤ x ≤ 14
Question 10
Solve: |x + 2| < 5
- A. x ≤ −7 or x ≥ 3
- B. x < 3
- C. −3 < x < 7
- D. −7 < x < 3
Question 11
Solve: |2x + 8| ≤ 4
- A. −12 ≤ x ≤ −4
- B. −6 ≤ x ≤ −2
- C. x ≤ −6 or x ≥ −2
- D. 2 ≤ x ≤ 6
Question 12
Solve: |x + 1| < 4
- A. x ≤ −5 or x ≥ 3
- B. −5 < x < 3
- C. −3 < x < 5
- D. x < 3
Question 13
Solve: |2x − 4| ≤ 6
- A. −5 ≤ x ≤ 1
- B. x ≤ −1 or x ≥ 5
- C. −2 ≤ x ≤ 10
- D. −1 ≤ x ≤ 5
Question 14
Solve: |x − 2| < 1
- A. 1 < x < 3
- B. x ≤ 1 or x ≥ 3
- C. x < 3
- D. −3 < x < −1
Question 15
Solve: |3x − 6| ≤ 9
- A. −1 ≤ x ≤ 5
- B. −5 ≤ x ≤ 1
- C. −3 ≤ x ≤ 15
- D. x ≤ −1 or x ≥ 5
Question 16
Solve: |x − 5| < 6
- A. x < 11
- B. −11 < x < 1
- C. x ≤ −1 or x ≥ 11
- D. −1 < x < 11
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