Absolute Value Equations Quiz

Solve the absolute value equation: |2x - 3| = 5

• x = 2, -4

• x = 1, -2

• x = 3, -5

• x = 4, -1

Answer explanation

To solve the absolute value equation |2x - 3| = 5, we consider two cases: 2x - 3 = 5 and 2x - 3 = -5. For the first case, solving for x gives x = 4. For the second case, solving for x gives x = -1. Therefore, the correct answer is x = 4, -1.

Solve the absolute value equation: |3x + 2| = 7

• x < -2/3 or x = 2/3

• x < -2/3 or x > 2/3

• x < -2/3 or x > -2/3

• x > -2/3 or x = 2/3

Answer explanation

To solve the absolute value equation |3x + 2| = 7, we consider two cases: 3x + 2 = 7 and 3x + 2 = -7. Solving these equations, we get x > -2/3 and x < -2/3, respectively. So, the correct answer is x < -2/3 or x > -2/3.

Solve the absolute value equation: |4x - 1| = 9

• x = 2.5, -2

• x = 1, -1

• x = 3, -3

• x = -2.5, 2

Answer explanation

The absolute value equation |4x - 1| = 9 can be solved by setting 4x - 1 equal to both 9 and -9. Solving these two equations gives us x = 2.5 and x = -2, respectively. Therefore, the correct answer is x = 2.5, -2.

Solve the absolute value equation: |5x + 4| = 3

• x = -1/5, 7/5

• x = 1/5, 7/5

• x = -1/5, -7/5

• x = -1/5, 1/5

Answer explanation

The absolute value equation |5x + 4| = 3 can be solved by setting 5x + 4 equal to both 3 and -3. Solving these two equations gives us x = -1/5 and x = -7/5 respectively. Therefore, the correct answer is x = -1/5, -7/5.

Solve the absolute value equation: |6x - 5| = 2

• x = 2/3, x = 1/5

• x = 5/6, x = 1/4

• x = 3/2, x = 1/3

• x = 7/6, x = 1/2

Answer explanation

To solve the absolute value equation |6x - 5| = 2, we consider two cases: 6x - 5 = 2 and 6x - 5 = -2. Solving the first case, we get x = 7/6. Solving the second case, we get x = 1/2. Therefore, the correct answer is x = 7/6, x = 1/2.

Solve the absolute value equation: |7x + 6| = 8

• x = -2/7, 2

• x = -8/7, 2

• x = 2/7, -2

• x = -2/7, 8

Answer explanation

To solve the absolute value equation |7x + 6| = 8, we consider two cases: 7x + 6 = 8 and 7x + 6 = -8. For the first case, we get x = 2/7, and for the second case, we get x = -2. Therefore, the correct answer is x = 2/7, -2.

Solve the absolute value equation: |8x - 7| = 1

• x = 1, 0.75

• x = 1, 0.5

• x = 1, -0.75

• x = -1, 0.75

Answer explanation

To solve the absolute value equation |8x - 7| = 1, we consider two cases: 8x - 7 = 1 and 8x - 7 = -1. For the first case, solving for x gives x = 1. For the second case, solving for x gives x = 0.75. Therefore, the correct answer is x = 1, 0.75.

Solve the absolute value equation: |9x + 8| = 6

• x = 2/9, 14/9

• x = -2/9, 14/9

• x = -2/9, -14/9, 2/9

• x = -2/9, -14/9

Answer explanation

To solve the absolute value equation |9x + 8| = 6, we consider two cases: 9x + 8 = 6 and 9x + 8 = -6. Solving these equations, we get x = -2/9 and x = -14/9, respectively. Therefore, the correct answer is x = -2/9, -14/9.

Solve the absolute value equation: |10x - 9| = 4

• x = 1.3, x = 0.5

• x = -0.5, x = 1.7

• x = 2.3, x = 0.2

• x = -1.3, x = 0.8

Answer explanation

The absolute value equation |10x - 9| = 4 can be solved by setting 10x - 9 equal to both 4 and -4. Solving these two equations gives us x = 1.3 and x = 0.5 respectively. Therefore, the correct answer is x = 1.3, x = 0.5.

Solve the absolute value equation: |11x + 10| = 12

• x < -10/11 or x > -10/11

• x < -11/10 or x > -11/10

• x < -12/11 or x > -12/11

• x < -10/11 or x > 10/11

Answer explanation

The absolute value equation |11x + 10| = 12 can be solved by setting 11x + 10 equal to both 12 and -12. Solving these two equations gives us x < -10/11 or x > -10/11. This matches the correct answer.