Interval Notation Help?

Question

6: Solve and write in interval notation: | x | – 2 < 7
(-9, 9)
(-∞, -5) U (9, ∞)
(-5, 9)
(-∞, 9) U (9, ∞)


7: Solve and write in interval notation: | 3x | + 5 > 14
(-∞, -19/3) U (3, ∞)
(-∞, -3) U (3, ∞)
(-3, 3)
(-19/3, 3)


8: Solve and write in interval notation: | 2x – 4 | ≤ 12
[-4, 8]
(-∞, -4] U [8, ∞)
[-8, 8]
(-∞, -8] U [8, ∞)


9: Solve and write in interval notation: | (3x) / 4 + 5 | < 1
(-∞, -5) U (1, ∞)
(-8, -16/3)
(-16/3, 16/3)
No solution


10: Solve and write in interval notation: -(1/6) + | 2 – x / 3 | > (1/2)
(-∞, ∞)
(-∞, 4) U (7, ∞)
(-∞, 4) U (8, ∞)
No solution


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

6. x<9 so (-infinity, 9) and then -x<9 or x>-9 so (-9,infinity)
6 is A

7.absolute value of 3x>9 so x>3 and x<-3 so (-3,3)
7 is C

8.| 2x – 4 | ≤ 12
2x-4≤ 12 so 2x≤ 16 so x≤ 8
-2x-4≤ 12 so -2x≤ 16 so x [-8,8]
8 is C

9. | (3x) / 4 + 5 | < 1
3x/4<-4
3x<-16
x<-5and 1/3
-3x/4<-4
-3x<-16
x>5 and 1/3
9 is C

10. -(1/6) + | 2 – x / 3 | > (1/2)
2-x/3>2/3
-x/3>2/3-6/3 or -x/3> -4/3
-x>-4
x<4
2+x/3>2/3
x/3>-4/3
x>-4
(-4,4) so no solution?