Solving Equations With Variables On Both Sides

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| By Simonedeitch
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Simonedeitch
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Questions and Answers
  • 1. 

    Do you have any questions about the video? Were there any problems that did not make sense?

  • 2. 

    Solve:  -7 - 4c = -c + 8

    • A.

      C = -5

    • B.

      C = -3

    • C.

      C = 3

    • D.

      C = 5

    Correct Answer
    A. C = -5
    Explanation
    To solve the equation, we need to isolate the variable c. First, we can combine like terms by adding c to both sides of the equation. This gives us -7 - 3c = 8. Next, we can simplify further by adding 7 to both sides, resulting in -3c = 15. To isolate c, we divide both sides of the equation by -3. This gives us c = -5. Therefore, the correct answer is c = -5.

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  • 3. 

    Solve:  -7p = -8p + 9

    • A.

      P = 3/5

    • B.

      P = -9

    • C.

      P = 9

    • D.

      P = -3/5

    Correct Answer
    C. P = 9
    Explanation
    The equation given is -7p = -8p + 9. To solve for p, we can start by simplifying the equation. By subtracting -8p from both sides of the equation, we get p = 9. Therefore, the correct answer is p = 9.

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  • 4. 

    Solve:  10t + 10 = -8 + 8t

    • A.

      T = -18

    • B.

      T = -9

    • C.

      T = 18

    • D.

      T = 9

    Correct Answer
    B. T = -9
    Explanation
    To solve the equation 10t + 10 = -8 + 8t, we need to simplify both sides of the equation. By combining like terms, we get 2t + 10 = -8. Next, we can isolate the variable by subtracting 10 from both sides, resulting in 2t = -18. Finally, we divide both sides by 2 to solve for t, giving us t = -9.

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  • 5. 

    How many solutions are there for the following equation:  -4c = 8 - 4c

    • A.

      No solutions

    • B.

      One solution

    • C.

      Infinitely many solutions

    Correct Answer
    A. No solutions
    Explanation
    The equation -4c = 8 - 4c can be simplified to 0 = 8, which is not possible. This means that there are no values of c that satisfy the equation, leading to the conclusion that there are no solutions.

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  • 6. 

    How many solutions are there for the following equation:  -5q - 9 = 4q

    • A.

      No solutions

    • B.

      One solution

    • C.

      Infinitely many solutions

    Correct Answer
    B. One solution
    Explanation
    The given equation is a linear equation. To solve it, we can combine like terms and isolate the variable. By adding 5q to both sides, we get -9 = 9q. Dividing both sides by 9, we find that q = -1. Therefore, there is one solution for the equation, which is q = -1.

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  • 7. 

    Is this an identity:  5 - 5z = -5z + 5

    • A.

      Yes

    • B.

      No

    Correct Answer
    A. Yes
    Explanation
    The given equation is an identity because both sides of the equation are equal when simplified. By rearranging the terms, we can see that 5 - 5z is equal to -5z + 5. This holds true for any value of z, making it an identity.

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