algebra 2 help?

Question

1: Write in interval notation: x < 2 or x > 1
(- ∞ , 2)
(1, 2)
(-∞ , ∞ )
(1, ∞ )


2: Write in interval notation: x < 2 AND x ≥ 1
[1, ∞ )
(1, 2)
(-∞ , ∞ )
[1, 2)


3: Write in interval notation: x < 3 OR x < -1
(-1, 3)
(-∞ , 3)
(-∞ , -1)
(-∞ , ∞ )


4: Write in interval notation: x > 2 OR x ≤ 2
[2, ∞ )
(-∞ , ∞ )
(-∞ , 2)
(-2, 2]


5: Write in interval notation: x ≤ 5 AND x > 3
(3, 5]
(-∞ , 5]
(-∞ , 3)
(-∞ , ∞ )


6: Write in interval notation: x < 5 AND x < 3
(-∞ , 3)
(-∞ , 5)
(3, 5)
(-∞ , ∞ )

Answer 1

1. x<2 or x>1
(1,2)

2. x<2 and x>=1
[1,2)

3.x<3 or x<-1
(-inf, 3)

4. x>2 or x<=2
(-inf, inf)

5. x<=5 and x>3
(3,5]

6. x<5 and x<3
(-inf, 3)

I suggest graphing these on a number line and then shading the appropriate areas to find out which intervals you need. (graph the inequality)

Answer 2

1: Write in interval notation: x < 2 or x > 1
(-∞ , ∞ )


2: Write in interval notation: x < 2 AND x ≥ 1
[1, 2)


3: Write in interval notation: x < 3 OR x < -1
(-∞ , 3)


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


5: Write in interval notation: x ≤ 5 AND x > 3
(3, 5]


6: Write in interval notation: x < 5 AND x < 3
(-∞ , 3)

Answer 3

1 (-inf,inf)

2 [1,2)

3 (-inf,3)

4 (-inf, inf)

5 (3,5]

6 (-inf,3)

Answer 4

1. (1,2)
2. (1,2)
3. (-1,3)
4. [2, ∞)
5. (- ∞, ∞)
6. (- ∞,3)