Interval notation extra credit!?

Question

1: Write in interval notation: x > 3 AND x ≤ 7
(-∞, 7)
(3, 7]
(-∞, ∞)
(3, ∞)


2: Write in interval notation: 4 > x OR 3 > x
(3, 4)
(-∞, 3)
(-∞, 4)
(-∞, ∞)


3: Write in interval notation: x ≤ -3 AND x > -10
(-10, -3]
(-∞, -3]
[-10, -3)
(-∞, ∞)


4: Write in interval notation: x > 2 OR 5 > x
(2, 5)
(-∞, ∞)
(-∞, 5)
(2, ∞)


5: Write in interval notation: x > 2 AND 5 > x
(2, 5)
(-∞, ∞)
(-∞, 5)
(2, ∞)


6: Write in interval notation: x > 2 OR 5 < x
(2, 5)
(-∞, ∞)
(-∞, 5)
(2, ∞)


7: Solve and write in interval notation: x − 3 > 8 AND x + 2 > 4
(-∞, ∞)
(2, ∞)
(2, 11)
(11, ∞)


8: Solve and write in interval notation: 7 ≥ x + 4 OR x − 3 < 2
(-∞, 5)
(-∞, ∞)
[3, 5)
(3, ∞)


9: Solve and write in interval notation: x / 2 ≤ -3 AND x − 5 < 2
(-∞, -3/2)
(-∞, -6]
(-∞, 7)
(-∞, ∞)


10: Solve and write in interval notation: -3 ≤ (x + 4) / 3 < -1
(-∞, ∞)
(-13, ∞)
[-13, -7)
[-13, -5)

Answer 1

I sure am glad they gave you such easy extra credit to complete over the holidays. I notice the notation ( is for >, [ is for greater than or equal too. ) is for <, ] is for less than or equal to.
Use that to solve such as 10. [-13, -7)
That is help, now get to work.

Answer 2

1: Write in interval notation: x > 3 AND x ≤ 7
(3, 7]

2: Write in interval notation: 4 > x OR 3 > x
(-∞, 4)

3: Write in interval notation: x ≤ -3 AND x > -10
(-10, -3]

4: Write in interval notation: x > 2 OR 5 > x
(-∞, ∞)

5: Write in interval notation: x > 2 AND 5 > x
(2, 5)

6: Write in interval notation: x > 2 OR 5 < x
(2, ∞)

7: Solve and write in interval notation: x − 3 > 8 AND x + 2 > 4
(11, ∞)

8: Solve and write in interval notation: 7 ≥ x + 4 OR x − 3 < 2
(-∞, 5)

9: Solve and write in interval notation: x / 2 ≤ -3 AND x − 5 < 2
(-∞, -6]

10: Solve and write in interval notation: -3 ≤ (x + 4) / 3 < -1
[-13, -7)

Answer 3

1: Write in interval notation: x > 3 AND x ≤ 7
(3, 7] ANS

2: Write in interval notation: 4 > x OR 3 > x
(-∞, ∞) ANS

10, -3] ANS

4: Write in interval notation: x > 2 OR 5 > x
(2, ∞) ANS

5: Write in interval notation: x > 2 AND 5 > x
(2, 5) ANS

6: Write in interval notation: x > 2 OR 5 < x
(2, ∞) ANS

7: Solve and write in interval notation: x − 3 > 8 AND x + 2 > 4
Solution:
x - 3 > 8
x > 8 + 3
x > 11

x + 2 > 4
x > 4 - 2
x > 2

ANS: (2, ∞)

8: Solve and write in interval notation: 7 ≥ x + 4 OR x − 3 < 2
Solution:
7 ≥ x + 4
7 - 4 ≥ x
3 ≥ x

x − 3 < 2
x < 2 + 3
x < 5
(-∞, 5) ANS

9: Solve and write in interval notation: x / 2 ≤ -3 AND x − 5 < 2
x / 2 ≤ -3 AND x − 5 < 2
x ≤ (-3)(2)
x ≤ -6

x - 5 < 2
x < 2 + 5
x < 7
ANS: (-∞, 7)

10: Solve and write in interval notation: -3 ≤ (x + 4) / 3 < -1
-3 ≤ (x + 4) / 3 < -1
-3(3) ≤ x + 4 < -1(3)
-9 - 4 ≤ x < -3 - 4
-13 ≤ x < -7
ANS: [-13, -7)

teddy boy

Answer 4

(-∞, ∞)
(-∞, 4)
(-10, -3]
(-∞, ∞)
(2, 5)