MAth hELP!!! PLEASE!!! :)?

Question

1. Which conjunction or disjunction is equivalent to Ix-9I < 11?
A. x - 9 < 11 and x + 9 > -11
B. x - 9 < 11 and x - 9 > -11
C. x - 9 < 11 or x 9 < -11
D. x - 9 < 11 or x - 9 > -11

2. Which conjunction or disjunction is equivalent to Ix+4I >= 1?
A. x + 4 >= 1 or x + 4 <= -1
B. x + 4 >=1 or x + 4 >= -1
C. x + 4 >= 1 and x + 4 >= -1
D. x + 4 >= 1 and x + 4 <= -1

Answer 1

|x-9|<11
let's imagine the number line
we are less than 11 units from positive 9 on the number line,
so we are between -2 and 20
or, x-9 < 11 and x-9 > -11
Which is exactly B.
2. |x+4|≥1
We are at least one unit away from -4 on the number line
thus
x+4≥1 or x+4≤-1
Which is A.

The rule is to think: If these two parts don't overlap, I need to use an "or". If they do overlap, I need to use an "and".
No number is both bigger than 1 and less than 0. And every number is either less than 1 or greater than 0. Look at your answer, and ask "does this make sense?". If you can't tell, try drawing a picture if it will help

Answer 2

1) B (less than are and)

2) A (greater than are or)

Answer 3

1) B

2) A

Answer 4

1) B

2) D

Answer 5

1. b
2.d

Answer 6

1) A
2)A

Answer 7

I don't know.