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Solving Linear Equations

Description: This quiz is designed to assess your understanding of solving linear equations. It covers various types of linear equations, including one-step equations, two-step equations, and equations with variables on both sides.
Number of Questions: 14
Created by:
Tags: algebra linear equations one-step equations two-step equations variables on both sides
Attempted 0/14 Correct 0 Score 0

Solve the equation: 3x + 5 = 17

  1. x = 4

  2. x = 5

  3. x = 6

  4. x = 7


Correct Option: A
Explanation:

To solve the equation, we need to isolate the variable x on one side of the equation. First, we subtract 5 from both sides: 3x + 5 - 5 = 17 - 5, which simplifies to 3x = 12. Then, we divide both sides by 3: 3x / 3 = 12 / 3, which gives us x = 4.

Solve the equation: 2(x - 3) = 10

  1. x = 5

  2. x = 6

  3. x = 7

  4. x = 8


Correct Option: D
Explanation:

To solve the equation, we first distribute the 2 to the terms inside the parentheses: 2x - 6 = 10. Then, we add 6 to both sides: 2x - 6 + 6 = 10 + 6, which simplifies to 2x = 16. Finally, we divide both sides by 2: 2x / 2 = 16 / 2, which gives us x = 8.

Solve the equation: 3x - 2 = 5x + 4

  1. x = -3

  2. x = -2

  3. x = -1

  4. x = 0


Correct Option: B
Explanation:

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 3x from both sides: 3x - 2 - 3x = 5x + 4 - 3x, which simplifies to -2 = 2x + 4. Then, we subtract 4 from both sides: -2 - 4 = 2x + 4 - 4, which gives us -6 = 2x. Finally, we divide both sides by 2: -6 / 2 = 2x / 2, which gives us x = -3.

Solve the equation: 2x + 3 = 4x - 5

  1. x = 4

  2. x = 5

  3. x = 6

  4. x = 7


Correct Option: A
Explanation:

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 2x from both sides: 2x + 3 - 2x = 4x - 5 - 2x, which simplifies to 3 = 2x - 5. Then, we add 5 to both sides: 3 + 5 = 2x - 5 + 5, which gives us 8 = 2x. Finally, we divide both sides by 2: 8 / 2 = 2x / 2, which gives us x = 4.

Solve the equation: 5(x + 2) = 3(x - 4)

  1. x = 10

  2. x = 11

  3. x = 12

  4. x = 13


Correct Option: C
Explanation:

To solve the equation, we first distribute the 5 and 3 to the terms inside the parentheses: 5x + 10 = 3x - 12. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 5x - 3x = -12 - 10, which simplifies to 2x = -22. Finally, we divide both sides by 2: 2x / 2 = -22 / 2, which gives us x = -11.

Solve the equation: 2(3x - 1) = 4(x + 2)

  1. x = 3

  2. x = 4

  3. x = 5

  4. x = 6


Correct Option: C
Explanation:

To solve the equation, we first distribute the 2 and 4 to the terms inside the parentheses: 6x - 2 = 4x + 8. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 6x - 4x = 8 + 2, which simplifies to 2x = 10. Finally, we divide both sides by 2: 2x / 2 = 10 / 2, which gives us x = 5.

Solve the equation: 3x + 5 = 2x - 7

  1. x = 12

  2. x = 13

  3. x = 14

  4. x = 15


Correct Option: A
Explanation:

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 2x from both sides: 3x + 5 - 2x = 2x - 7 - 2x, which simplifies to x + 5 = -7. Then, we subtract 5 from both sides: x + 5 - 5 = -7 - 5, which gives us x = -12.

Solve the equation: 4(x - 3) = 2(x + 5)

  1. x = 17

  2. x = 18

  3. x = 19

  4. x = 20


Correct Option: C
Explanation:

To solve the equation, we first distribute the 4 and 2 to the terms inside the parentheses: 4x - 12 = 2x + 10. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 4x - 2x = 10 + 12, which simplifies to 2x = 22. Finally, we divide both sides by 2: 2x / 2 = 22 / 2, which gives us x = 11.

Solve the equation: 5x - 2 = 3x + 8

  1. x = 5

  2. x = 6

  3. x = 7

  4. x = 8


Correct Option: A
Explanation:

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 3x from both sides: 5x - 2 - 3x = 3x + 8 - 3x, which simplifies to 2x - 2 = 8. Then, we add 2 to both sides: 2x - 2 + 2 = 8 + 2, which gives us 2x = 10. Finally, we divide both sides by 2: 2x / 2 = 10 / 2, which gives us x = 5.

Solve the equation: 2(x + 3) = 4(x - 1)

  1. x = 5

  2. x = 6

  3. x = 7

  4. x = 8


Correct Option: C
Explanation:

To solve the equation, we first distribute the 2 and 4 to the terms inside the parentheses: 2x + 6 = 4x - 4. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 2x - 4x = -4 - 6, which simplifies to -2x = -10. Finally, we divide both sides by -2: -2x / -2 = -10 / -2, which gives us x = 5.

Solve the equation: 3(x - 2) = 2(x + 4)

  1. x = 10

  2. x = 11

  3. x = 12

  4. x = 13


Correct Option: C
Explanation:

To solve the equation, we first distribute the 3 and 2 to the terms inside the parentheses: 3x - 6 = 2x + 8. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 3x - 2x = 8 + 6, which simplifies to x = 14. Finally, we check our answer by substituting x = 14 back into the original equation: 3(14 - 2) = 2(14 + 4), which simplifies to 3(12) = 2(18), which is true.

Solve the equation: 4(x + 1) = 2(2x - 3)

  1. x = 5

  2. x = 6

  3. x = 7

  4. x = 8


Correct Option: C
Explanation:

To solve the equation, we first distribute the 4 and 2 to the terms inside the parentheses: 4x + 4 = 4x - 6. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 4x - 4x = -6 - 4, which simplifies to 0 = -10. This equation has no solution, so there is no value of x that satisfies the equation.

Solve the equation: 5(x - 1) = 3(2x + 4)

  1. x = 7

  2. x = 8

  3. x = 9

  4. x = 10


Correct Option: C
Explanation:

To solve the equation, we first distribute the 5 and 3 to the terms inside the parentheses: 5x - 5 = 6x + 12. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 5x - 6x = 12 + 5, which simplifies to -x = 17. Finally, we multiply both sides by -1 to isolate x: -x * -1 = 17 * -1, which gives us x = -17.

Solve the equation: 2(x + 2) = 3(x - 1) + 4

  1. x = 5

  2. x = 6

  3. x = 7

  4. x = 8


Correct Option: B
Explanation:

To solve the equation, we first distribute the 2 and 3 to the terms inside the parentheses: 2x + 4 = 3x - 3 + 4. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 2x - 3x = -3 + 4 - 4, which simplifies to -x = -3. Finally, we multiply both sides by -1 to isolate x: -x * -1 = -3 * -1, which gives us x = 3.

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