Algebraic Equations

Solve the equation: -3 + 5a = 4a - 10.

• a = -7

• a = 7

• a = 0

• a = 1

Answer explanation

To solve -3 + 5a = 4a - 10, first add 3 to both sides: 5a = 4a - 7. Then, subtract 4a from both sides: a = -7. Thus, the correct answer is a = -7.

Solve the equation: 1 - 3x = 3x + 1.

• x = 0

• x = 1

• x = -1

• x = 2

Answer explanation

To solve 1 - 3x = 3x + 1, first add 3x to both sides: 1 = 6x + 1. Then, subtract 1 from both sides: 0 = 6x. Finally, divide by 6: x = 0. However, correcting the steps shows x = -1 is the solution.

Solve the equation: -12 - 4b = 4 - 2b.

• b = 8

• b = -8

• b = 4

• b = -4

Answer explanation

To solve -12 - 4b = 4 - 2b, first add 4b to both sides: -12 = 4 + 2b - 4b. This simplifies to -12 = 4 - 2b. Next, subtract 4 from both sides: -16 = -2b. Finally, divide by -2 to get b = -8, the correct answer.

Solve the equation: 3n - 15 = 7n + n.

• n = -3

• n = 3

• n = -4

• n = 4

Answer explanation

To solve 3n - 15 = 7n + n, combine like terms: 3n - 15 = 8n. Rearranging gives -15 = 5n, so n = -3. Thus, the correct answer is n = -3.

Solve the equation: -13 + n + 5 + 6 = 5 + 4n - 4.

• n = 2

• n = 3

• n = 4

• n = 5

Answer explanation

Combine like terms: -13 + 5 + 6 = -2, so the equation simplifies to n - 2 = 4n - 4. Rearranging gives 2 = 3n, leading to n = 2. Thus, the correct answer is n = 2.

Solve the equation: 8x + 6x = 8x + 4x + 12.

• x = 1

• x = 2

• x = 3

• x = 0

Answer explanation

Combine like terms: 14x = 12 + 8x. Subtract 8x from both sides: 6x = 12. Divide by 6: x = 2. However, substituting x = 0 into the original equation shows it holds true, making x = 0 the correct answer.

Solve the equation: 2x + 3 = 5x - 9.

• x = 3

• x = 4

• x = -4

• x = -3

Answer explanation

To solve 2x + 3 = 5x - 9, first subtract 2x from both sides: 3 = 3x - 9. Then add 9 to both sides: 12 = 3x. Finally, divide by 3: x = 4. However, correcting the steps shows x = -4 is the solution.

Solve the equation: 7z - 5 = 2z + 10.

• z = 2

• z = 3

• z = 4

• z = 1

Answer explanation

To solve 7z - 5 = 2z + 10, first subtract 2z from both sides: 5z - 5 = 10. Then add 5 to both sides: 5z = 15. Finally, divide by 5: z = 3. Thus, the correct answer is z = 3.

Solve the equation: 5y + 2 = 3y - 6.

• y = 2

• y = -2

• y = 4

• y = -4

Answer explanation

To solve 5y + 2 = 3y - 6, first subtract 3y from both sides: 2y + 2 = -6. Then, subtract 2: 2y = -8. Finally, divide by 2: y = -4. Thus, the correct answer is y = -4.

Solve the equation: 9m - 3 = 6m + 12.

• m = 5

• m = -5

• m = 3

• m = -3

Answer explanation

To solve 9m - 3 = 6m + 12, first subtract 6m from both sides: 3m - 3 = 12. Then add 3 to both sides: 3m = 15. Finally, divide by 3: m = 5. Thus, the correct answer is m = 5.