Inequalities: Compound And Absolute Value

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| By Tom Plocker

Tom Plocker

Community Contributor

Quizzes Created: 1 | Total Attempts: 206

Questions: 6 | Attempts: 207 | Updated: Mar 19, 2023

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Questions and Answers

1.

* Solve:
- A.
  
  X < 1 or x > 5
- B.
  
  1 < x < 5
- C.
  
  X < -1 or x > -5
- D.
  
  X < -5 or x > -1
Correct Answer
A. X < 1 or x > 5

Explanation
The given answer x < 1 or x > 5 is correct because it represents the correct solution to the given inequality x < 1 or x > 5. This means that x can be any value that is less than 1 or greater than 5.

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2.

* Solve:
- A.
  
  -9 ≤ n ≤ -1
- B.
  
  N ≤ -9 or n ≥ -1
- C.
  
  N ≤ -1 or n ≥ 9
- D.
  
  -1 ≤ n ≤ 9
Correct Answer
A. -9 ≤ n ≤ -1

Explanation
The correct answer is -9 ≤ n ≤ -1. This is because the inequality -9 ≤ n ≤ -1 means that n can take any value between -9 and -1, including -9 and -1 themselves. It satisfies all the given conditions in the question.

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3.

* Solve:
- A.
  
  K ≤ - 2 or k ≥ 3
- B.
  
  -2 ≤ k ≤ 3
- C.
  
  K ≤ -3 or k ≥ 2
- D.
  
  -3 ≤ k ≤ 2
Correct Answer
A. K ≤ - 2 or k ≥ 3

Explanation
The correct answer is k ≤ -2 or k ≥ 3. This is because the given inequality represents two separate ranges for the variable k. The first range, k ≤ -2, includes all values of k that are less than or equal to -2. The second range, k ≥ 3, includes all values of k that are greater than or equal to 3. Therefore, the correct answer is the combination of these two ranges, k ≤ -2 or k ≥ 3.

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4.

* Solve:
- A.
  
  X < 1 or x ≥ 2
- B.
  
  1 < x < 2
- C.
  
  X < 2 or x ≥ 1
- D.
  
  No solution!
Correct Answer
A. X < 1 or x ≥ 2

Explanation
The given answer, "x < 1 or x ≥ 2", is correct because it represents the solution to the given inequalities. The statement "x < 1 or x ≥ 2" means that x can be any value that is less than 1 or any value that is greater than or equal to 2. This covers all possible values of x that satisfy the given inequalities.

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5.

* Solve:
- A.
  
  -1 ≤ w < 5
- B.
  
  -2 ≤ w < 10
- C.
  
  W ≤ -1 or w ≥ 5
- D.
  
  No solution!
Correct Answer
A. -1 ≤ w < 5

Explanation
The given inequalities state that w must be greater than or equal to -1 and less than 5. This means that w can take any value between -1 and 5, including -1 but not including 5. Therefore, the correct answer is -1 ≤ w < 5.

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6.

Which inequality is represented by the graph below:
- A.
- B.
- C.
- D.
Correct Answer
A.