Multi Step Inequalities Quiz - By Melissa Barnhart

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| By Melissa Barnhart

Melissa Barnhart

Community Contributor

Quizzes Created: 1 | Total Attempts: 284

Questions: 6 | Attempts: 284 | Updated: Mar 20, 2023

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Multi Step Inequalities Quiz - By Melissa Barnhart - Quiz

Solving Multi-Step Inequalities

Questions and Answers

1.

Solve. 5(x - 2) > 20
- A.
  
  X < 6
- B.
  
  X > 2
- C.
  
  X < 2
- D.
  
  X > 6
Correct Answer
D. X > 6

Explanation
The given inequality is 5(x - 2) > 20. To solve this, we first distribute 5 to both terms inside the parentheses, resulting in 5x - 10 > 20. Next, we add 10 to both sides to isolate the variable, which gives us 5x > 30. Finally, we divide both sides by 5 to solve for x, giving us x > 6.

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1
0
2.

Solve. -5p - 5 - 2p < -33
- A.
  
  P > -4
- B.
  
  P < 5.14
- C.
  
  P > 4
- D.
  
  P < 5
Correct Answer
C. P > 4

Explanation
The given inequality is solved by combining like terms and isolating the variable p. By adding 5 to both sides and combining like terms, we get -7p - 5 < -33. Then, by adding 7p to both sides and subtracting 33 from both sides, we get -5 < 7p - 33. By adding 33 to both sides, we get 28 < 7p. Finally, by dividing both sides by 7, we get p > 4.

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3.

Solve. 3(x + 2) - 4 < 92
- A.
  
  X < -30
- B.
  
  X < 30
- C.
  
  X > 30
- D.
  
  X > -30
Correct Answer
B. X < 30

Explanation
To solve the inequality, we first distribute the 3 to both terms inside the parentheses: 3x + 6 - 4 < 92. Simplifying further, we have 3x + 2 < 92. Next, we subtract 2 from both sides of the inequality: 3x < 90. Finally, we divide both sides by 3 to isolate x: x < 30. Therefore, the correct answer is x < 30.

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4.

Solve for x:4(x - 1) + 3 > 15
- A.
  
  X > 4
- B.
  
  X > -4
- C.
  
  X < 4
- D.
  
  X < -4
Correct Answer
A. X > 4

Explanation
To solve the inequality 4(x - 1) + 3 > 15, we first distribute 4 to the terms inside the parentheses, resulting in 4x - 4 + 3 > 15. Simplifying further, we get 4x - 1 > 15. Adding 1 to both sides, we have 4x > 16. Finally, dividing both sides by 4, we find that x > 4. Therefore, the correct answer is x > 4.

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5.

Solve for x:-10x + 6 + 8x ≤ 20
- A.
  
  X ≤ -7
- B.
  
  X ≥ -7
- C.
  
  X ≥ 7
- D.
  
  X ≤ 7
Correct Answer
B. X ≥ -7

Explanation
The given inequality is solved by combining like terms and isolating the variable x. By subtracting 6 from both sides of the inequality, we get -10x + 8x ≤ 14. Simplifying further, we have -2x ≤ 14. Dividing both sides by -2, we find that x ≥ -7. Therefore, the answer is x ≥ -7.

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6.

Which answer represents the graph above?
- A.
  
  X > 3
- B.
  
  X ≤ 3
- C.
  
  X ≥ 3
Correct Answer
C. X ≥ 3

Explanation
The graph above represents the solution set where x is greater than or equal to 3. This is because the line on the graph is solid and includes the point (3,0), indicating that 3 is included in the solution set. Therefore, the correct answer is x ≥ 3.

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Current Version
Mar 20, 2023

Quiz Edited by
ProProfs Editorial Team
Oct 31, 2017

Quiz Created by
Melissa Barnhart

Multi Step Inequalities Quiz - By Melissa Barnhart

Solve. 5(x - 2) > 20

Solve. -5p - 5 - 2p < -33

Solve. 3(x + 2) - 4 < 92

Solve for x:4(x - 1) + 3 > 15

Solve for x:-10x + 6 + 8x ≤ 20

Which answer represents the graph above?