Question

1. Which expresses the given inequality in interval notation?

Answer 1

Answer:

The corrext answer is C.

Answer 2

1)  x < 4  the answer is    Option C: x E(-infinity,4)  (it is strict)
2)  2x +6 < 8, and  2x < 8 - 6 = 2, and x<2/2=1
the answer is
D. x E (-infinity, 1)
3)  X greater than or equal to 8 and  x <  - 4
X greater than  8  means x ≥ 8
so we have x ≥ 8 and   x <  - 4
so the answer is 
B. x E (-4,8]
 4) 
7 > x + 6 or x -2 greater than or equal to 3,
7 > x + 6 or x -2 ≥ 3

7 -6> x, and 1>x

x -2 ≥ 3   x≥ 3+2=5
finally
x<1 and x≥5   

the answer is
C.x E (1,5]
5)

|x+3| > 12, 
|x+3| = { -(x+3) if x+3<0 or  (x+3)  if x+3>0}

so, it is  -(x+3)>12 is equivalent to (x+3)< -12  or (x+3)>12
the answer is
B. x + 3 > 12 or x + 3 <-12