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)