Interval Notation?

Question

11: Solve and write in interval notation: | 4 – 3x | + 1/2 < -2
(-∞, -3/2) U (3/2, ∞)
(1/2, 13/3)
(-∞, ∞)
No solution


12: Solve and write in interval notation: | 3 – 2x | – 8 ≥ 1
(-∞, -5/2] U [5/2, ∞)
(-∞, -3] U [6, ∞)
[-3, 6]
No solution

Answer 1

| 4 – 3x | + 1/2 < -2
|4- 3x| < -5/2
no solution. An absolute value is always positive, so it cannot be less than a negative number.

|3 – 2x | – 8 ≥ 1
|3- 2x| ≥ 9
3-2x ≥ 9.... and .... -9≥ 3-2x
-6 ≥ 2x ....and.....2x ≥ 12
-3 ≥ x ....and ....x ≥ 6
(-∞, -3] U [6, ∞)