Interval Notation?

Question

1: Write in interval notation: | x | ≤ 3
(-∞, -3] U [3, ∞)
(-∞, ∞)
[-3, 3]
No solution


2: Write in interval notation: | x | ≥ 4
(-∞, -4] U [4, ∞)
No solution
[-4, 4]
(-∞, ∞)


3: Solve and write in interval notation: | 4x | > -12
(-∞, -3) U (3, ∞)
No solution
(-3, 3)
(-∞, ∞)


4: Solve and write in interval notation: | x – 3 | < 9
(-∞, -6) U (12, ∞)
(-∞, ∞)
(-∞, -9) U (9, ∞)
(-6, 12)


5: Solve and write in interval notation: | 3x – 2 | ≥ 4
(-∞, -2] U [2/3, ∞)
(-∞, -2/3] U [2, ∞)
(-∞, -2] U [6, ∞)
[-2/3, 2]

Answer 1

#1 [-3, 3]

#2 (-∞, -4] U [4, ∞)

#3 (-∞, -3) U (3, ∞)

#4 (-6, 12)

#5 (-∞, -2/3] U [2, ∞)

Answer 2

Heather has all except 3 right. It should be (neg inf, pos inf)

[You and Heather are aware that any absolute value will be zero or greater; therefore it must also be greater than -12.]