Solving One Step Inequalites

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| By Philip Benanti
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Philip Benanti
Community Contributor
Quizzes Created: 18 | Total Attempts: 27,123
Questions: 18 | Attempts: 339

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Equation Quizzes & Trivia

Questions and Answers
  • 1. 

    X / 9 > 10

    • A.

      X < 90

    • B.

      X > 90

    • C.

      X > 1.11

    • D.

      X > 10

    Correct Answer
    B. X > 90
    Explanation
    The correct answer is x > 90 because when we divide x by 9 and the result is greater than 10, it means that x must be greater than 90. If x were less than 90, the result of the division would be less than 10.

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  • 2. 

    X / 6 > 7

    • A.

      X > 42

    • B.

      X > 7

    • C.

      X > 1.17

    • D.

      X < 42

    Correct Answer
    A. X > 42
    Explanation
    The given inequality states that x divided by 6 is greater than 7. To solve this inequality, we can multiply both sides of the inequality by 6 to isolate x. This gives us x > 42, which means that x is greater than 42. Therefore, the correct answer is x > 42.

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  • 3. 

    X / -3 > 2

    • A.

      X > -6

    • B.

      X < 2

    • C.

      X < -6

    • D.

      X > -0.67

    Correct Answer
    C. X < -6
    Explanation
    The given inequality states that x divided by -3 is greater than 2. To solve this inequality, we can multiply both sides by -3, but since we are multiplying by a negative number, the inequality sign will flip. This gives us x < -6, which means that x is less than -6. Therefore, the correct answer is x < -6.

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  • 4. 

    X / -3 > -8

    • A.

      X < -8

    • B.

      X > 2.67

    • C.

      X > 24

    • D.

      X < 24

    Correct Answer
    D. X < 24
    Explanation
    The given inequality states that x divided by -3 is greater than -8. To solve this inequality, we can multiply both sides by -3, which reverses the inequality sign. Therefore, we get x is less than 24. This means that any value of x that is less than 24 will satisfy the inequality.

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  • 5. 

    X / -5 > -3

    • A.

      X < 15

    • B.

      X < 0.60

    • C.

      X > -3

    • D.

      X > 15

    Correct Answer
    A. X < 15
    Explanation
    The given inequality states that x divided by -5 is greater than -3. To solve this inequality, we can multiply both sides by -5 to get x by itself. When we multiply both sides by -5, we need to reverse the inequality sign. So, x is less than 15, which means the correct answer is x < 15.

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  • 6. 

    X / 10 > 3

    • A.

      X > 0.30

    • B.

      X < 30

    • C.

      X > 3

    • D.

      X > 30

    Correct Answer
    D. X > 30
    Explanation
    The correct answer is x > 30 because if we divide both sides of the inequality x / 10 > 3 by 10, we get x > 30. This means that x must be greater than 30 in order for the inequality to be true.

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  • 7. 

    X / 9 > 9

    • A.

      X > 1

    • B.

      X > 81

    • C.

      X > 9

    • D.

      X < 81

    Correct Answer
    B. X > 81
    Explanation
    The given inequality states that x divided by 9 is greater than 9. To solve this inequality, we can multiply both sides of the inequality by 9, which gives us x is greater than 81. Therefore, the correct answer is x > 81.

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  • 8. 

    When you multiply both sides of any inequality by a negative number, you need to ________ the inequality symbol.

    Correct Answer
    flip
    Explanation
    When you multiply both sides of any inequality by a negative number, you need to flip the inequality symbol. This is because multiplying by a negative number reverses the order of the numbers. For example, if we have the inequality 3 > 2 and we multiply both sides by -1, we get -3 < -2. So, in order to maintain the correct order of the numbers, we need to flip the inequality symbol.

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  • 9. 

    Solve:  y - 16 < 12

    • A.

      Y < -28

    • B.

      Y > 28

    • C.

      Y < 28

    Correct Answer
    C. Y < 28
    Explanation
    The given inequality is y - 16 < 12. To solve this inequality, we can add 16 to both sides to isolate the variable y. This gives us y < 28, which means that y is less than 28. Therefore, the correct answer is y < 28.

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  • 10. 

    Write an inequality for "a number minus 14 is more than 35."

    • A.

      14 - n ≥ 35

    • B.

      N - 14 ≥ 35

    • C.

      N - 14 < 35

    • D.

      N - 14 > 35

    Correct Answer
    D. N - 14 > 35
    Explanation
    The correct answer is n - 14 > 35. This inequality represents the statement "a number minus 14 is more than 35." By subtracting 14 from a number (n) and setting it greater than 35, we are expressing that the result of the subtraction is greater than 35.

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  • 11. 

    Write an inequality for "six times a number is at most 91."

    • A.

      6k ≤ 91

    • B.

      6k ≥ 91

    • C.

      6k < 91

    • D.

      6k > 91

    Correct Answer
    A. 6k ≤ 91
    Explanation
    The inequality 6k ≤ 91 represents the statement "six times a number is at most 91." This means that when the number is multiplied by 6, the result is less than or equal to 91.

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  • 12. 

    Solve.  x - (-4) < 12

    • A.

      X < 8

    • B.

      X < 16

    • C.

      X > 8

    • D.

      X > 16

    Correct Answer
    A. X < 8
    Explanation
    The given inequality is x - (-4) < 12. Simplifying this, we get x + 4 < 12. Subtracting 4 from both sides, we have x < 8. Therefore, the correct answer is x < 8.

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  • 13. 

    Solve.  y - (-3) > -16

    • A.

      Y < -13

    • B.

      Y < -19

    • C.

      Y > -19

    • D.

      Y > -13

    Correct Answer
    C. Y > -19
    Explanation
    The given inequality is y - (-3) > -16. Simplifying this, we get y + 3 > -16. Subtracting 3 from both sides, we have y > -19. Therefore, the correct answer is y > -19.

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  • 14. 

    Solve.  z - 5 ≥ 11

    • A.

      Z ≥ 6

    • B.

      Z ≥ 16

    • C.

      Z ≤ 16

    • D.

      Z ≥ -6

    Correct Answer
    B. Z ≥ 16
    Explanation
    The inequality z - 5 ≥ 11 can be solved by adding 5 to both sides of the inequality, resulting in z ≥ 16. This means that any value of z that is greater than or equal to 16 satisfies the inequality.

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  • 15. 

    Solve.  6x > 12

    • A.

      X > -2

    • B.

      X > -6

    • C.

      X > 2

    • D.

      X > 18

    Correct Answer
    C. X > 2
    Explanation
    The given inequality is 6x > 12. To solve for x, we divide both sides of the inequality by 6, resulting in x > 2. This means that any value of x that is greater than 2 will satisfy the inequality.

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  • 16. 

    Solve.  4b > -36

    • A.

      B > -9

    • B.

      B < -9

    • C.

      B > 9

    • D.

      B < 9

    Correct Answer
    A. B > -9
    Explanation
    The given inequality is 4b > -36. To solve this inequality, we divide both sides by 4 (since it is a positive number), giving us b > -9. This means that b is greater than -9.

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  • 17. 

    Solve.  -5k ≤ 20

    • A.

      K ≤ -4

    • B.

      K ≥ 4

    • C.

      K ≤ 4

    • D.

      K ≥ -4

    Correct Answer
    D. K ≥ -4
    Explanation
    The given inequality states that -5k is less than or equal to 20. To solve for k, we need to isolate it on one side of the inequality. By dividing both sides of the inequality by -5, we get k greater than or equal to -4. Therefore, the correct answer is k ≥ -4.

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  • 18. 

    X / -9 > 4

    • A.

      X > -36

    • B.

      X < 4

    • C.

      X > -0.44

    • D.

      X < -36

    Correct Answer
    B. X < 4
    Explanation
    Let's solve the inequality step by step:Start with �−9>4−9x​>4.Multiply both sides by -9. Since we're multiplying by a negative number, the direction of the inequality sign flips.
    �<4x<4

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  • Current Version
  • Mar 01, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Nov 20, 2014
    Quiz Created by
    Philip Benanti
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