Multi Step Inequalities Quiz - By Melissa Barnhart

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| By Melissa Barnhart
M
Melissa Barnhart
Community Contributor
Quizzes Created: 1 | Total Attempts: 282
Questions: 6 | Attempts: 282

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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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  • 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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