Section 4.1 - Interpreting The Solution Of A Linear Equation

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Interpreting the solution of a linear equation is a topic in algebra therefore if you are a student in need of practice then this quiz is for you. If you are prepared to test your knowledge try it out.


Questions and Answers
  • 1. 

    Solve 4x + 2 =18

    • A. 

      X = 5

    • B. 

      X = 4

    • C. 

      X = 9

    • D. 

      X = 16

    Correct Answer
    B. X = 4
    Explanation
    To solve the equation 4x + 2 = 18, we need to isolate the variable x.
    First, we subtract 2 from both sides of the equation to get 4x = 16.
    Then, we divide both sides by 4 to solve for x, which gives us x = 4.
    Therefore, the correct answer is x = 4.

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  • 2. 

    Estimate the solution to 6x + 2 = 5

    • A. 

      X = 2

    • B. 

      X = 5

    • C. 

      X = 6

    • D. 

      X = 1/2

    Correct Answer
    D. X = 1/2
    Explanation
    To estimate the solution to the equation 6x + 2 = 5, we need to isolate the variable x. By subtracting 2 from both sides of the equation, we get 6x = 3. To solve for x, we divide both sides of the equation by 6, which gives us x = 1/2. Therefore, the correct answer is x = 1/2.

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  • 3. 

    Sophie is buying a gold chain.  The gold chain costs $2.50 per cm.  How many cm can she buy if she has $30 to spend?

    • A. 

      30cm

    • B. 

      250cm

    • C. 

      12cm

    • D. 

      6cm

    Correct Answer
    C. 12cm
    Explanation
    Sophie has $30 to spend and the gold chain costs $2.50 per cm. To find out how many cm she can buy, we divide the total amount she has by the cost per cm. So, $30 divided by $2.50 equals 12. Therefore, Sophie can buy 12 cm of the gold chain with her $30.

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  • 4. 

    A plumber charges a $75 flat fee plus $25 per hour for each job.  Which linear equation represents the cost of a job that lasts "t" hours?

    • A. 

      C = 25t + 75

    • B. 

      C = 75t + 25

    • C. 

      C = 25t

    • D. 

      C = 100t

    Correct Answer
    A. C = 25t + 75
    Explanation
    The equation c = 25t + 75 represents the cost of a job that lasts "t" hours. The $75 flat fee is added to the $25 per hour charge for each hour of work. This equation follows the form of a linear equation, where the cost (c) is equal to the rate per hour (25t) multiplied by the number of hours (t), with the flat fee (75) added.

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  • 5. 

    Find the x-intercept of the equation y = 3x - 6

    • A. 

      (0, -6)

    • B. 

      (-6, 0)

    • C. 

      (2, 0)

    • D. 

      (0, 2)

    Correct Answer
    C. (2, 0)
    Explanation
    The x-intercept of an equation is the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. In the given equation y = 3x - 6, when y = 0, we have 0 = 3x - 6. Solving this equation, we find x = 2. Therefore, the x-intercept is (2, 0).

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  • 6. 

    Which function will not have an x-intercept?

    • A. 

      Y = x

    • B. 

      Y = -2x

    • C. 

      Y = 5

    • D. 

      X = 2

    Correct Answer
    C. Y = 5
    Explanation
    The equation y = 5 represents a horizontal line with a y-coordinate of 5. Since the line is parallel to the x-axis, it will never intersect the x-axis and therefore will not have an x-intercept.

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  • 7. 

    Nate is saving up to purchase a new computer.  He has $175 already and can save $20 per month.  How long will it take him to save $515?

    • A. 

      17 months

    • B. 

      34 months

    • C. 

      26 months

    • D. 

      20 months

    Correct Answer
    A. 17 months
    Explanation
    Nate already has $175 and can save $20 per month. To calculate how long it will take him to save $515, we can subtract his current savings from the target amount and then divide it by his monthly savings. $515 - $175 = $340. $340 ÷ $20 = 17. Therefore, it will take Nate 17 months to save $515.

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  • 8. 

    Use algebra to solve the equation 4x + 3 = -13

    • A. 

      X = -2.5

    • B. 

      X = -16

    • C. 

      X = -4

    • D. 

      X = -3

    Correct Answer
    C. X = -4
    Explanation
    To solve the equation 4x + 3 = -13, we need to isolate the variable x. First, we subtract 3 from both sides of the equation to get 4x = -16. Then, we divide both sides by 4 to solve for x. This gives us x = -4. Therefore, the correct answer is x = -4.

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  • 9. 

    Find the x-intercept of the equation y =  x + 3

    • A. 

      (3, 0)

    • B. 

      (0, 0)

    • C. 

      (-3, 0)

    • D. 

      (0, 3)

    Correct Answer
    C. (-3, 0)
    Explanation
    The x-intercept of an equation represents the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y=0 and solve for x. In this equation, when y=0, x+3=0, which gives x=-3. Therefore, the x-intercept is (-3, 0).

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  • 10. 

    A cell-phone company charges $10 per month plus $0.10 per minute.  How many minutes can Tori use if she budgeted $30 per month for her cell-phone bill?

    • A. 

      2000 min

    • B. 

      300 min

    • C. 

      20 min

    • D. 

      200 min

    Correct Answer
    D. 200 min
    Explanation
    Tori has a budget of $30 per month for her cell-phone bill. The cell-phone company charges $10 per month plus $0.10 per minute. To find out how many minutes Tori can use, we subtract the fixed monthly charge of $10 from her budget, which leaves $20. Then, we divide this remaining amount by the cost per minute, which is $0.10. By doing this calculation, we find that Tori can use 200 minutes within her budget of $30 per month.

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