Algebra Test

Result

Algebra Test - 15

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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)

E
(-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
φ

D
(-, 7] U [9, )

E
[7, 9]

Solution

2x - 3 < 11 and -8x - 10 < -82
2x < 14 and -8 x < -72
x < 7 and x > 9
Hence x ∈ φ
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, )

E
(8, -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,)

E
(-1, 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)

E
(-, 3) U [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, )

E
(-, -1) U (9, )

Solution

-12 < (7x - 5) 9
-7 < 7x 14
-1 < x 2
(-1, 2]
Question 7
1 / -0

Which of the following number lines represents the solution of the inequality - 19 < 4d - 7 < 13?

A

B

C

D

E

Solution

-19 < 4d -7 < 13
-19 + 7 < 4d -7 + 7 < 13 + 7
- 12 < 4d < 20
-3 < d < 5 (On dividing by 4)
Question 8
1 / -0

Which of the following inequalities is represented by the above number line?

A
-19 < 4x - 713

B
12 < 5 x + 1 < 8

C
16 x + 3 < 11

D
-12 2x + 3 5

E
-9 3x + 1 2

Solution

From the graph, we get - 3 < x 5
On comparing the values of the inequalities, we get
- 19 < 4x - 7 13.
- 12 < 4x 20
- 3 < x 5
Question 9
1 / -0

Which of the following graphs satisfies the inequality 3x + 4 19?

A

B

C

D

E

Solution

3x + 4 19
3x 15
x 5
Question 10
1 / -0

Which of the following graphs satisfies the inequality - 7 < 2 - 3x < 11?

A

B

C

D

E

Solution

- 7 < 2 + 3x < 11
-2 -2 -2

-3 < x < 3
Question 11
1 / -0

Which of the following sets of solution is represented by the above graph?

A
(-4, 5)

B
[-4, 5)

C
[-4, 5]

D
(-, -4] U [5, )

E
[-, -4) U (5, ]

Solution

The left arrow shows all the values including -4 and less.
The right arrow shows all the values including 5 and more.
So, (-, -4] U [5,) is the correct answer.
Question 12
1 / -0

Which of the following solution sets is represented by the above graph?

A
(-2, 6]

B
(-2, 6)

C
[-2, 6]

D
(-, -2) U [6, )

E
[-, -2] U [6, )

Solution

The graph lies between -2 and 6 and includes 6 as the solution.
So, (-2, 6] is the correct answer.
Question 13
1 / -0

Which of the following sets of solutions is represented by the above graph?

A
(3, 7)

B
(3, 7]

C
[3, 7)

D
[3, 7]

E
(-, 3] U [7, )

Solution

The graph includes all values except the values that lie between 3 and 7.
So, (-, 3] U [7, ) is the correct answer.
Question 14
1 / -0

Which of the following graphs shows the solution of the inequalities x + 3 < -1 and - 3x - 6?

A

B

C

D

E

Solution

x + 3 - 1 or - 3x < - 6
x -1 - 3 or x > 2
x - 4 or x > 2
So, the required value is R - (-4, 2]. So option (1) is correct.
Question 15
1 / -0

Which of the following graphs represents the solution set of 0 x 5?

A

B

C

D

E

Solution

The inequality 0 x 5 means all values from 0 to 5 including 0 and 5.
Question 16
1 / -0

Which of the following graphs represents the solution for x < - 1 and x > 3?

A

B

C

D

E

Solution

x < - 1 or x > 3 means either less than - 1 or greater than 3 excluding the two values. Option `4` is the answer.
Question 17
1 / -0

Which of the following sets of solution represents the above graph?

A
x < 6

B
x > 6

C
x 6

D
x 6

E
0 x 6

Solution

The inequality shows the values greater than 6 including 6. So, x 6 is the correct answer.
Question 18
1 / -0

Which of the following graphs represents the solution of the inequality - 2x - 6?

A

B

C

D

E

Solution

- 2x - 6
- x - 3
x 3
Question 19
1 / -0

Which of the following graphs represents the inequality (-, -3] U (4, )?

A

B

C

D

E

Solution

(-, -3] U (4, ) means all values less than 3 including 3 and all values greater than 4.
Question 20
1 / -0

Which of the following represents the solution of the above graph?

A
[-2, 3]

B
[-2, 3)

C
(-, -2) U (3, ]

D
(-2, 3)

E
(-, -2] U (3, )

Solution

The graph shows all the values between -2 and 3 including -2.