Algebra Test

Result

Algebra Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following sets of values of x satisfies the inequalities - 10 - 2x < 6 and 6 x + 12 < - 6?

A
[-8, 3)

B
(8, -3]

C
(-8, 3)

D
(-8,-3)

Solution

- 10 -2x < 6 and 6 x + 12 < - 6
- 2x < 16 and 6 x < - 18
x > - 8 and x < - 3
= - 8 < x < -3 = (-8, -3)
Question 2
1 / -0

Which of the following sets of values of x satisfies the inequalities 2x - 3 < 11 and -8x - 10 < -82?

A
(- ∞, -7) U (-7, ∞)

B
(-7, -9)

C
(-, 7 ) U (9, )

D
(- ∞, 7] U [9, ∞)

Solution

2x - 3 < 11 or -8x - 10 < -82
2x < 14 or -8 x < -72
x < 7 or x > 9
Hence x ∈ (-∞, 7) U (9, ∞)
Question 3
1 / -0

What is the value of x in the inequalities - 5x - 8 ≤" - 68 and 11 x - 12 < -100?

A
(-8, 12)

B
(-∞, - 8) U [12, ∞)

C
[-∞, -8] U [12, ∞]

D
(-∞,8) U (12, ∞)

Solution

- 5x - 8 ≤ - 68 or 11 x - 12 < - 100 - 5x ≤ - 60 or 11 x < - 88x ≥ 12 or x < - 8 = ( - ∞, - 8) U [12, ∞)
Question 4
1 / -0

What is the value of x in the inequalities 2x - 1 < - 5 and 3x + 2 > 5?

A
(-∞, - 2) U ( - 1 , ∞)

B
(-∞, - 2 ) U (1, ∞)

C
[-2, -1]

D
(-∞, 1) U [2,∞)

Solution

2x -1 < - 5 or 3x + 2 >, 5
2x < - 4 or 3x > 3
x < -2 or x > 1 = (-∞, -2) U (1, ∞)
Question 5
1 / -0

Which of the following sets of values satisfies the inequality -20 < 4x - 8 < 12?

A
(3, 5)

B
(-∞, -3) (5, ∞)

C
[-∞, 3) U (4, ∞)

D
(-3, 5)

Solution

-20 < 4x - 8 < 12
- 20 + 8 < 4x < 12 + 8
- 12 < 4x < 20
-3 < x < 5
Hence x ∈ (-3, 5)
Question 6
1 / -0

Which of the following sets of values of x satisfies the inequality -12 < (7x - 5) ≤ 9?

A
(-1, 2]

B
(-1, ∞) U (∞, 2)

C
(1, -2)

D
(-∞, 1) U (12, ∞)

Solution

-12 < (7x - 5) ≤ 9
-7 < 7x ≤ 14
-1 < x ≤ 2
(-1, 2]