Section 4.2 - Solving Linear Equations Using Inverse Operations

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  • 1/10 Questions

    Which inverse operation should be applied first to solve 3x + 5 = 10?

    • Addition
    • Subtraction
    • Division
    • Multiplication
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About This Quiz

This quiz focuses on solving linear equations using inverse operations, including writing equations from word problems and solving for specific variables.

Linear Equations Quizzes & Trivia

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  • 2. 

    Solve 5x + 3 =  23

    • X = 5.2

    • X = 20

    • X = 4

    • X = 6

    Correct Answer
    A. X = 4
    Explanation
    To solve the equation 5x + 3 = 23, we need to isolate the variable x. We can do this by subtracting 3 from both sides of the equation, giving us 5x = 20. Then, we divide both sides of the equation by 5 to solve for x, which gives us x = 4.

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  • 3. 

    The equation C = 2.5p + 75 can be used to represent the cost, C to rent the rollar skating rink when p attend.  How much will it cost if 100 people attend.

    • $250

    • $325

    • $75

    • $175

    Correct Answer
    A. $325
    Explanation
    The equation C = 2.5p + 75 represents the cost, C, to rent the roller skating rink when p people attend. In this equation, the coefficient of p is 2.5, indicating that the cost increases by $2.5 for each additional person. By substituting p = 100 into the equation, we can calculate the cost. C = 2.5(100) + 75 = 250 + 75 = $325. Therefore, if 100 people attend, it will cost $325.

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  • 4. 

    Write an equation for the following problem, "Half of a number minus 6 is 20"

    • (x - 6) / 2 = 20

    • X - 6 = 20

    • 2x - 6 = 20

    • X/2 - 6 = 20

    Correct Answer
    A. X/2 - 6 = 20
    Explanation
    The equation (x/2 - 6 = 20) represents the given problem accurately. It states that "half of a number minus 6 is 20". By dividing the number x by 2 and then subtracting 6, we should get the result of 20.

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  • 5. 

    Solve x/4 + 6= 9

    • X = 4

    • X = 0.5

    • X = 60

    • X = 12

    Correct Answer
    A. X = 12
    Explanation
    To solve the equation x/4 + 6 = 9, we need to isolate the variable x. We can start by subtracting 6 from both sides of the equation, which gives us x/4 = 3. To solve for x, we can multiply both sides of the equation by 4, resulting in x = 12. Therefore, the correct answer is x = 12.

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  • 6. 

    The equation C = 10 + 0.25m represents the cost, C of a cell phone bill if m minutes are used.  Which equation represents a bill of $25?

    • 25 = 10 + 0.25m

    • C = 10 + 0.25(25)

    • C = 10 + 25

    • 25 = 0.25m

    Correct Answer
    A. 25 = 10 + 0.25m
    Explanation
    The equation C = 10 + 0.25m represents the cost, C of a cell phone bill if m minutes are used. To find the equation that represents a bill of $25, we substitute 25 for C in the equation. By substituting 25 for C, the equation becomes 25 = 10 + 0.25m. This equation represents a bill of $25.

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  • 7. 

    Solve   x/5 + 2 = 7

    • X = 25

    • X = 45

    • X = 1

    • X = 5

    Correct Answer
    A. X = 25
    Explanation
    To solve the equation x/5 + 2 = 7, we need to isolate the variable x. First, we subtract 2 from both sides of the equation, which gives us x/5 = 5. Next, we multiply both sides of the equation by 5 to eliminate the fraction, resulting in x = 25. Therefore, the correct answer is x = 25.

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  • 8. 

    Which inverse operation should be applied first to solve 5 - 3e = 15

    • Addition

    • Subtraction

    • Multiplication

    • Division

    Correct Answer
    A. Subtraction
    Explanation
    To solve the equation 5 - 3e = 15, we need to isolate the variable "e". The inverse operation of subtraction is addition, so the first step is to add 5 to both sides of the equation. This will cancel out the 5 on the left side, leaving us with -3e = 10. Now we can proceed to solve for "e" by dividing both sides by -3.

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  • 9. 

    The equation P=2L + 2W can be used tp fomd the perimeter of a rectangle.  A rectangular shaped playground is enclosed by a fence that is 500m.  The length of the playground is 120m.  Use the equation to determine the width of the playground.

    • 190m

    • 260m

    • 180m

    • 130m

    Correct Answer
    A. 130m
    Explanation
    The equation P=2L + 2W represents the perimeter of a rectangle, where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter of the playground is 500m and the length is 120m. By substituting these values into the equation, we can solve for the width. Plugging in P=500m and L=120m, we get 500m=2(120m) + 2W. Simplifying this equation, we have 500m=240m + 2W. Subtracting 240m from both sides, we get 260m=2W. Dividing both sides by 2, we find that the width of the playground is 130m.

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  • 10. 

    Solve  (x - 3) / 5 = 10

    • X = 13

    • X = 65

    • X = 53

    • X = 47

    Correct Answer
    A. X = 53
    Explanation
    To solve the equation (x - 3) / 5 = 10, we can start by multiplying both sides of the equation by 5 to eliminate the fraction. This gives us x - 3 = 50. Then, we can add 3 to both sides to isolate x, resulting in x = 53. Thus, the correct answer is x = 53.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 07, 2008
    Quiz Created by
    Seixeiroda
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