Equations With Variables On Both Sides?

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| By Bhawnakul14

Bhawnakul14

Community Contributor

Quizzes Created: 15 | Total Attempts: 70,272

Questions: 8 | Attempts: 437 | Updated: Mar 19, 2023

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Equations With Variables On Both Sides? - Quiz

Play this quiz and learn more about both side equation and variables!

Questions and Answers

1.

9x - 12 = 3x
- A.
  
  2
- B.
  
  -2
- C.
  
  1
- D.
  
  -1
Correct Answer
A. 2

Explanation
By solving the equation 9x - 12 = 3x, we can find the value of x. First, we can simplify the equation by subtracting 3x from both sides, which gives us 6x - 12 = 0. Then, we can add 12 to both sides to isolate the variable, resulting in 6x = 12. Finally, we divide both sides by 6 to solve for x, getting x = 2. Therefore, the correct answer is 2.

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2.

8x - 12 = 15x - 4x
- A.
  
  4
- B.
  
  -3/5
- C.
  
  -4
- D.
  
  +3/5
Correct Answer
C. -4

Explanation
In the given equation, we have 8x - 12 on the left side and 15x - 4x on the right side. To solve the equation, we need to simplify both sides by combining like terms. On the left side, we have 8x - 12, and on the right side, we have 15x - 4x which simplifies to 11x. Therefore, the equation becomes 8x - 12 = 11x. To isolate x, we subtract 11x from both sides, resulting in -3x - 12 = 0. Finally, we add 12 to both sides, giving us -3x = 12. Dividing both sides by -3, we find that x = -4.

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3.

11 + 6x = 2x - 13
- A.
  
  4
- B.
  
  -4
- C.
  
  6
- D.
  
  -6
Correct Answer
D. -6

Explanation
To find the value of x in the equation 11 + 6x = 2x - 13, we need to isolate the variable x. First, we can simplify the equation by combining like terms. By subtracting 2x from both sides, we get 9 + 4x = -13. Next, by subtracting 9 from both sides, we obtain 4x = -22. To solve for x, we divide both sides by 4, which gives us x = -5.5. However, since the given answer choices are integers, we round down to the nearest whole number, resulting in x = -6.

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4.

-5x = 9 - 2x
- A.
  
  9/7
- B.
  
  -9/7
- C.
  
  3
- D.
  
  -3
Correct Answer
D. -3

Explanation
The given equation is -5x = 9 - 2x. To solve for x, we can combine like terms by adding 2x to both sides of the equation, which gives -3x = 9. Then, we divide both sides of the equation by -3 to isolate x, resulting in x = -3. Therefore, the correct answer is -3.

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5.

-8x - 10 = 4x + 14
- A.
  
  6
- B.
  
  2
- C.
  
  -6
- D.
  
  -2
Correct Answer
D. -2

Explanation
To solve the equation -8x - 10 = 4x + 14, we need to isolate the variable x. First, we can add 8x to both sides of the equation to eliminate the variable on the left side. This gives us -10 = 12x + 14. Next, we can subtract 14 from both sides to move the constant term to the right side. This gives us -24 = 12x. Finally, we can divide both sides by 12 to solve for x. This gives us x = -2. Therefore, the correct answer is -2.

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6.

10x - 5 = 21 - 3x
- A.
  
  2
- B.
  
  2
- C.
  
  3
- D.
  
  3
- E.
  
  4
- F.
  
  4
- G.
  
  -2
- H.
  
  -2
Correct Answer(s)
A. 2
B. 2

Explanation
The given equation is a linear equation in one variable. To solve it, we can start by simplifying both sides of the equation. By adding 3x to both sides and adding 5 to both sides, we get 13x = 26. Dividing both sides by 13, we find that x = 2. Therefore, the equation is satisfied when x = 2.

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7.

-12x = 14 - 5x
- A.
  
  1
- B.
  
  2
- C.
  
  -2
- D.
  
  3
Correct Answer
C. -2

Explanation
To solve the equation -12x = 14 - 5x, we need to isolate the variable x. We can do this by combining like terms. Subtracting -5x from both sides of the equation, we get -12x + 5x = 14. Simplifying this, we have -7x = 14. To solve for x, we divide both sides of the equation by -7. This gives us x = -2. Therefore, the correct answer is -2.

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8.

4x + 12 = -3x - 6 + 4x
- A.
  
  4
- B.
  
  3
- C.
  
  -6
- D.
  
  2
Correct Answer
C. -6

Explanation
In the given equation, 4x + 12 = -3x - 6 + 4x, we need to simplify and solve for x. By combining like terms, we can simplify the equation to 8x + 12 = -6. Next, by subtracting 12 from both sides, we get 8x = -18. Finally, dividing both sides by 8, we find that x = -2.25. Therefore, the answer -6 is incorrect and does not correspond to any step in the solution process.

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