If you were to explain them all I would be EXTREMELY appreciative(ha ha :) For any help that is given I thank you in advance!
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]
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
13: The graph of #1 consists of:
a closed circle on -3 with shading to the left and a closed circle on 3, shading to the right
the entire number line shaded
a closed circle on -3, a closed circle on 3, and shading in between
an empty number line (nothing shaded)
14: The graph of #2 consists of:
a closed circle on -4, shading to the left, a closed circle on 4, shading to the right
the entire number line shaded
a closed circle on -4, a closed circle on 4, shading in between
an empty number line (nothing shaded)
15: The graph of #3 consists of:
an open circle on -3, with shading to the left and an open circle on 3, with shading to the right
the entire number line shaded
an open circle on -3, an open circle on 3, with shading in between
an empty number line (nothing shaded)
16: The graph of #4 consists of:
an open circle on -9, shading to the left, and an open circle on 9, shading to the right
an open circle on -6, shading to the left, and an open circle on 12, shading to the right
an open circle on -6, an open circle on 12, with shading in between
an empty number line (nothing shaded)
17: The graph of #9 consists of:
an open circle on -5, shading to the left, and an open circle on 1, shading to the right
the entire number line shaded
an open circle on -8, an open circle on -16/3, with shading in between
an open circle on -16/3, an open circle on 16/3, with shading in between
18: The graph of #11 consists of:
an open circle on -3/2, shading to the left, and an open circle on 3/2, shading to the right
the entire number line shaded
an open circle on 1/2, an open circle on 13/3, with shading in between
an empty number line (nothing shaded)
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