Absolute Value Equations and Inequalities

Solve the absolute value equation: |2x - 5| = 7.

• x = 8, -5

• x = 6, -1

• x = 4, -2

• x = 2, -3

Solve the absolute value equation: |3x + 2| = 10.

• x < -2/3 or x > -2/3

• x < 2/3 or x > 2/3

• x < -10 or x > -10

• x < -2/3 or x > -2/3

Solve the absolute value equation: |4x - 3| = 1.

• x = 1, -0.5

• x = 1, 0.5

• x = 2, 0.5

• x = 0, 0.5

Solve the absolute value equation: |5x + 1| = 9.

• x = 8/5, -2

• x = 7/5, -3

• x = -8/5, 2

• x = 10/5, -1

Solve the absolute value equation: |6x - 4| = 12.

• x = 4/3, -8/3

• x = 12/3, -6/3

• x = 2/3, -2/3

• x = 8/3, -4/3

Solve the absolute value inequality: |2x - 3| < 5.

• x < 2/3 or x > 2/3

• x < 1/2 or x > 1/2

• x < 3/2 or x > 3/2

• x < -3/2 or x > 3/2

Solve the absolute value inequality: |3x + 1| > 7.

Solve the absolute value inequality: |4x - 2| ≤ 6.

• x < 0.5 or x ≥ 0.5

• x < 0.5 and x > 0.5

• x ≤ 0.5 or x ≥ 0.5

• x < 0.5 or x > 0.5

Solve the absolute value inequality: |5x + 4| ≥ 10.

• x ≥ -2.8 or x ≤ 1.2

• x ≤ -2.8 or x ≥ 1.2

• x ≤ -2.8 or x ≥ 1.2

• x ≤ -2.8 or x ≤ 1.2

Solve the absolute value inequality: |6x - 5| ≠ 8.

• x = 8

• x = 2/3 and x = -13/6

• x ≠ 2/3 and x ≠ -13/6

• x = -8