Question

1. Which expresses the given inequality in interval notation?

x < 4

Option A: x E(4,infinity)

Option B: x E [4, infinity)

Option C: x E(-infinity,4)

Option D: x E (-infinity , 4]

2. Which is the solution set to the given inequality?
2x +6 < 8

a. x E(-infinity,1]
B. x E (1, infinity)
C. x E [ 1, infinity]
D. x E (-infinity, 1)

3. Which represents the given compound inequality in interval notation?
X greater than or equal to x < -4
A. x E (-infinity,-4) U [8, infinity)
B. x E (-4,8]
C.x E [-4,8)
D.x E ( I infinity,-4] U (8, infinity)

4. Which is the solution set of the given compound inequality?
7 > x + 6 or x -2 greater than or equal to 3
A. x E [1,5)
B. x E (-infinity,1) U [ 5,infinity)
C.x E (1,5]
D. x E (- infinity, 1) n [ 5, infinity)

5. Which conjunction or disjunction is equivalent to the given absolute value inequality?
|x+3| > 12
A. x + 3 > 12 and x + 3 <-12
B. x + 3 > 12 or x + 3 <-12
C. x + 3 < 12 or x + 3 > -12
D. x + 3 < 12 and X + 3 > -12

Answer 1

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