Solving Equations With Variables On Both Sides
This quiz focuses on solving algebraic equations with variables on both sides, assessing skills in isolating variables and determining solution types or identities. It is essential for enhancing problem-solving abilities in algebra.
- 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 = -5Explanation
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.Rate this question:
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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 = 9Explanation
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.Rate this question:
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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 = -9Explanation
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.Rate this question:
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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 solutionsExplanation
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.Rate this question:
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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 solutionExplanation
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.Rate this question:
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- 7.
Is this an identity: 5 - 5z = -5z + 5
- A.
Yes
- B.
No
Correct Answer
A. YesExplanation
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.Rate this question:
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Current Version
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Mar 21, 2023Quiz Edited by
ProProfs Editorial Team -
Sep 16, 2013Quiz Created by
Simonedeitch
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