Absolute Value Equations and Inequalities

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

• x = 2, -3

• x = 4, -2

• x = 6, -1

• x = 8, -5

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

• x > 2/3 or x < -2/3.

• x > -2/3 or x < 2/3.

• x = -8/3, x = 4

• x = 8/3, x = -4

Solve the absolute value equation: |4x - 3| = 2

• x = 5/4, x = 1/4

• x = 3, x = 3/4.

• x = 5/4, x = -1/4

• x = -1, x = -1/4.

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

• x = 7/5, -3

• x = 6/5, -4

• x = 8/5, -2

• x = 9/5, -1

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

• -1 < x < 4

• (-inf, -1) U (4, inf)

• x < 1 or x > -4

• x < 3/2 or x > 5

Solve the absolute value inequality: |3x + 4| > 8

• x < -4/3 or x < 8

• x < -4/3 or x > 8

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

• x ≤ 0.5 or x > 0.5.

Solve the absolute value inequality: |5x + 3| ≥ 7

• x ≤ -2/5 or x ≤ -4/5

Graph the solution set of the absolute value inequality: |3x + 2| ≤ 6

• -2 ≤ x ≤ 6

• -6 ≤ x ≤ 2/3

• -8/3 ≤ x ≤ 4/3

• -8/3 < x < 2

|x - 4| = 3

can be stated as the set of points whose distance from ______ is equal to ______.

• -4; 3

• 4; 3

• 3; -4

• 3; 4