Absolute Value Equations

Solve the inequality |3x + 2| < 5.

• -3 < x < 1

• -7/3 < x < 1

• -7/3 < x < 2

• -5 < x < 1

If |2y - 1| = 7, what are the possible values of y?

• y = 4, -3

• y = 0, -7

• y = 2, -5

• y = 6, -1

Find all solutions to the equation |4z - 1| = 3.

• z = 2, z = -2

• z = -3, z = 4

• z = 0, z = 1

• z = 1, z = -1

A temperature sensor reads a value of |x - 20| = 15. What are the possible temperatures?

• 0, 40

• 10, 25

• 15, 30

• 5, 35

Solve the inequality |5a + 3| ≥ 8.

• a ≤ 0

• a ≤ -1

• a ≤ 3

• The solution is a ≤ 1 or a ≤ -2.

If |2b + 4| = 10, what are the possible values of b?

• 8, -12

• 5, -3

• 1, -9

• 3, -7

Find all solutions to the equation |6c - 2| = 4.

• c = 2, c = -2

• c = 3, c = -3

• c = 0, c = 4

• c = 1, c = -1

A distance from home is given by |d - 30| = 25. What are the possible distances?

• 20, 50

• 5, 55

• 15, 45

• 10, 40

Solve the inequality |7x - 5| < 2.

• 3/7 < x < 1

• x < 3/7

• -1 < x < 3/7

• x > 1

If |3y - 2| = 6, what are the possible values of y?

• y = 2, y = -4

• y = -1

• y = 5

• y = 0