just abrain buster :P see if you can do it:D?

Question

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


2: Write in interval notation: | 2x | < 6
(-∞, ∞)
(-∞, -3) U (3, ∞)
(-3, 3)
No solution


3: Solve and write in interval notation: | x + 5 | ≤ 4
[-9, -1]
(-∞, -9] U [1, ∞)
(-∞, -1] U [1, ∞)
[-1, 1]


4: Solve and write in interval notation: | x | - 2 > 9
(-7, 11)
(-11, 11)
(-∞, -11) U (11, ∞)
(-∞, -7) U (11, ∞)


5: Solve and write in interval notation: | -3x | + 2 ≤ 8
[-2, 10/3]
[-2, 2]
(-∞, -2] U [10/3, ∞)
(-∞, -2] U [2, ∞)


6: Solve and write in interval notation: 2 + | x/3 - 1 | > 6
(-9, 15)
(-3, 3)
(-∞, -3) U (3, ∞)
(-∞, -9) U (15, ∞)


7: Solve and write in interval notation: -1 + | 1/3 - x/2 | > -11/12
(-∞, 1/2) U (5/6, ∞)
(-1, 7/3)
(-∞, -1) U (7/3, ∞)
(1/2, 5/6)


8: Solve and write in interval notation: | 3 - x | > 7
(-∞, ∞)
(-4, 10)
(-∞, -4) U (4, ∞)
(-∞, -4) U (10, ∞)

Answer 1

Rule of thumb for absolute inequalities:
For a positive constant c:

1) | x | ≤ c translates to an AND. This translates to

x ≤ c AND x ≥ -c, which can also be written as the compound inequality

-c ≤ x ≤ c

Or, in interval notation,

[-c, c]

2) | x | ≥ c translates to an OR. This translates to

x ≥ c OR x ≤ -c

In interval notation, this is

(-∞, -c] U [c, ∞)

Answer 2

1: Write in interval notation: | x | ≥ 3
(-∞, -3] U [3, ∞)
2: Write in interval notation: | 2x | < 6
(-3, 3)
3: Solve and write in interval notation: | x + 5 | ≤ 4
[-9, -1]
4: Solve and write in interval notation: | x | - 2 > 9
(-∞, -11) U (11, ∞)

5: Solve and write in interval notation: | -3x | + 2 ≤ 8
(-∞, -2] U [2, ∞)
6: Solve and write in interval notation: 2 + | x/3 - 1 | > 6
(-∞, -9) U (15, ∞)


7: Solve and write in interval notation: -1 + | 1/3 - x/2 | > -11/12
(-∞, 1/2) U (5/6, ∞)

Answer 3

1 is c