1

Solve the following linear inequations in R

12x < 50, when

i. x ∈ R

ii. x ∈ Z

iii. x ∈ N

view answer >
2

Solve the following linear inequations in R

–4x > 30, when

i. x ∈ R

ii. x ∈ Z

iii. x ∈ N

view answer >
3

Solve the following linear inequations in R

4x – 2 < 8, when

i. x ∈ R

ii. x ∈ Z

iii. x ∈ N

view answer >
4

Solve the following linear inequations in R

3x – 7 > x + 1

view answer >
5

Solve the following linear inequations in R

x + 5 > 4x – 10

view answer >
6

Solve the following linear inequations in R

3x + 9 ≥ –x + 19

view answer >
7

Solve the following linear inequations in R

view answer >

8

Solve the following linear inequations in R

view answer >

9

Solve the following linear inequations in R

–(x – 3) + 4 < 5 – 2x

view answer >
10

Solve the following linear inequations in R

view answer >

11

Solve the following linear inequations in R

view answer >

12

Solve the following linear inequations in R

view answer >

13

Solve the following linear inequations in R

view answer >

14

Solve the following linear inequations in R

view answer >

15

Solve the following linear inequations in R

view answer >

16

Solve the following linear inequations in R

view answer >

17

Solve the following linear inequations in R

view answer >

18

Solve the following linear inequations in R

view answer >

19

Solve the following linear inequations in R

view answer >

20

Solve the following linear inequations in R

view answer >

21

Solve the following linear inequations in R

view answer >

22

Solve the following linear inequations in R

view answer >

23

Solve the following linear inequations in R

view answer >

24

Solve the following linear inequations in R

view answer >

25

Solve the following linear inequations in R

view answer >

26

Solve the following linear inequations in R

view answer >

27

Solve the following linear inequations in R

view answer >

28

Solve the following linear inequations in R

view answer >

1

Solve each of the following system of inequations in R

x + 3 > 0, 2x < 14

view answer >
2

Solve each of the following system of inequations in R

2x – 7 > 5 – x, 11 – 5x ≤ 1

view answer >
3

Solve each of the following system of inequations in R

x – 2 > 0, 3x < 18

view answer >
4

Solve each of the following system of inequations in R

2x + 6 ≥ 0, 4x – 7 < 0

view answer >
5

Solve each of the following system of inequations in R

3x – 6 > 0, 2x – 5 > 0

view answer >
6

Solve each of the following system of inequations in R

2x – 3 < 7, 2x > –4

view answer >
7

Solve each of the following system of inequations in R

2x + 5 ≤ 0, x – 3 ≤ 0

view answer >
8

Solve each of the following system of inequations in R

5x – 1 < 24, 5x + 1 > –24

view answer >
9

Solve each of the following system of inequations in R

3x – 1 ≥ 5, x + 2 > –1

view answer >
10

Solve each of the following system of inequations in R

11 – 5x > –4, 4x + 13 ≤ –11

view answer >
11

Solve each of the following system of inequations in R

4x – 1 ≤ 0, 3 – 4x < 0

view answer >
12

Solve each of the following system of inequations in R

x + 5 > 2(x + 1), 2 – x < 3(x + 2)

view answer >
13

Solve each of the following system of inequations in R

2(x – 6) < 3x – 7, 11 – 2x < 6 – x

view answer >
14

Solve each of the following system of inequations in R

15

Solve each of the following system of inequations in R

, 2(2x + 3) < 6(x – 2) + 10

view answer >
16

Solve each of the following system of inequations in R

view answer >

17

Solve each of the following system of inequations in R

view answer >

18

Solve each of the following system of inequations in R

view answer >

19

Solve each of the following system of inequations in R

10 ≤ –5(x – 2) < 20

view answer >
20

Solve each of the following system of inequations in R

–5 < 2x – 3 < 5

view answer >
21

Solve each of the following system of inequations in R

view answer >

1

Solve each of the following system of equations in R.

2

Solve each of the following system of equations in R.

view answer >

3

Solve each of the following system of equations in R.

view answer >

4

Solve each of the following system of equations in R.

view answer >

5

Solve each of the following system of equations in R.

view answer >

6

Solve each of the following system of equations in R.

view answer >

7

Solve each of the following system of equations in R.

view answer >

8

Solve each of the following system of equations in R.

view answer >

9

Solve each of the following system of equations in R.

view answer >

10

Solve each of the following system of equations in R.

view answer >

11

Solve each of the following system of equations in R.

view answer >

12

Solve each of the following system of equations in R.

view answer >

13

Solve each of the following system of equations in R.

view answer >

1

Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.

view answer >
2

Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.

view answer >
3

Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.

view answer >
4

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.

view answer >
5

A solution is to be kept between 86^{o} and 95^{o}F. What is the range of temperature in degree Celsius, if the Celsius (C)/Fahrenheit (F) conversion formula is given by

6

A solution is to be kept between 30^{o}C and 35^{o}C. What is the range of temperature in degree Fahrenheit?

7

To receive grade ‘A’ in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four papers, find the minimum marks that she must score in the last paper to get grade ‘A’ in the course.

view answer >
8

A company manufactures cassettes and its cost and revenue functions for a week are and R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?

view answer >
9

The longest side of a triangle is three times the shortest side, and the third side is 2 cm shorter than the longest side if the perimeter of the triangle at least 61 cm, Find the minimum length of the shortest-side.

view answer >
10

How many liters of water will have to be added to 1125 liters of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

view answer >
11

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 liters of the 8% solution, how many liters of 2% solution will have to be added?

view answer >
12

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading is 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level is normal.

view answer >
1

Represent to solution set of the following inequations graphically in two dimensional plane:

x + 2y – 4 ≤ 0

view answer >
2

Represent to solution set of the following inequations graphically in two dimensional plane:

x + 2y ≥ 6

view answer >
3

Represent to solution set of the following inequations graphically in two dimensional plane:

x + 2 ≥ 0

view answer >
4

Represent to solution set of the following inequations graphically in two dimensional plane:

x – 2y < 0

view answer >
5

Represent to solution set of the following inequations graphically in two dimensional plane:

– 3x + 2y ≤ 6

view answer >
6

Represent to solution set of the following inequations graphically in two dimensional plane:

x ≤ 8 – 4y

view answer >
7

Represent to solution set of the following inequations graphically in two dimensional plane:

0 ≤ 2x – 5y + 10

view answer >
8

Represent to solution set of the following inequations graphically in two dimensional plane:

3y > 6 – 2x

view answer >
9

Represent to solution set of the following inequations graphically in two dimensional plane:

y> 2x – 8

view answer >
10

Represent to solution set of the following inequations graphically in two dimensional plane:

3x – 2y ≤ x + y – 8

view answer >
1

Solve the following systems of linear inequaitons graphically.

2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0

view answer >
1

Solve the following systems of linear inequaitons graphically.

2x + 3y≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0

view answer >
1

Solve the following systems of linear inequaitons graphically.

x – y ≤ 1, x + 2y≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0

view answer >
1

Solve the following systems of linear inequaitons graphically.

x + y ≥ 1, 7x + 9y ≤ 63, x ≤6, y ≤ 5, x ≥ 0, y ≥ 0

view answer >
1

Solve the following systems of linear inequaitons graphically.

2x + 3y≤35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

view answer >
2

how that the solution set of the following linear inequations is empty set :

x – 2y ≥ 0, 2x – y ≤ –2, x ≥ 0, y ≥ 0

view answer >
2

how that the solution set of the following linear inequations is empty set :

x + 2y≤ 3, 3x + 4y≥ 12, y ≥ 1, x ≥ 0, y ≥ 0

view answer >
3

Find the linear inequations for which the shaded area in Fig. 15.41 is the solution set. Draw the diagram of the solution set of the linear inequations.

view answer >

4

Find the linear inequations for which the solution set is the shaded region given in Fig. 15.42.

view answer >

5

Show that the solution set of the following linear inequations is an unbounded set :

x + y ≥ 9, 3x + y ≥ 12, x ≥ 0, y ≥ 0.

view answer >
6

solve the following systems of inequations graphically :

2x + y ≥ 8, x + 2y ≥ 8, x + y ≤ 6

view answer >
6

solve the following systems of inequations graphically :

12 + 12y ≤ 840, 3x + 6y ≤ 300,8x + 4y ≤ 480, x ≥ 0, y ≥ 0

view answer >
6

solve the following systems of inequations graphically :

x + 2y≤ 40,3x + y ≥ 30, 4x + 3y≥ 60, x ≥ 0, y ≥ 0

view answer >
6

solve the following systems of inequations graphically :

5x + y ≥ 10, 2x + 2y ≥ 12, x + 4y ≥ 12, x ≥ 0, y ≥ 0

view answer >
7

Show that the following system of linear equations has no solution :

x + 2y ≥ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1.

view answer >
8

Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y≥ 8, x + 2y≥ 10, x ≥ 0, y ≥ 0.

view answer >
1

Write the solution set of the inequation .

view answer >
2

Write the solution set of the inequation .

view answer >
3

Write the set of values of x satisfying the inequation .

view answer >
4

Write the solution set of the inequation .

view answer >
5

Write the set of values of x satisfying and .

view answer >
6

Write the solution set of the inequation .

view answer >
7

Write the number of integral solutions of .

view answer >
8

Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and .

view answer >
9

Write the solution set of .

view answer >
10

Write the solution set of the inequation .

view answer >
1

view answer >

Mark the Correct alternative in the following:

If x < 7, then

view answer >

2

view answer >

Mark the Correct alternative in the following:

If −3x + 17 < −13, then

view answer >

3

view answer >

Mark the Correct alternative in the following:

Given that x, y and b are real numbers and x < y, b > 0, then

view answer >

4

view answer >

Mark the Correct alternative in the following:

If x is a real number and , then

view answer >

5

view answer >

Mark the Correct alternative in the following:

If x and a are real numbers such that a > 0 and , then

view answer >

6

view answer >

Mark the Correct alternative in the following:

If , then

view answer >

7

view answer >

Mark the Correct alternative in the following:

If , then

view answer >

8

view answer >

Mark the Correct alternative in the following:

The inequality representing the following graph is

view answer >

9

view answer >

Mark the Correct alternative in the following:

The linear inequality representing the solution set given in Fig. 15.44 is

view answer >

10

view answer >

Mark the Correct alternative in the following:

The solution set of the inequation is

view answer >

11

view answer >

Mark the Correct alternative in the following:

If , then

view answer >

12

view answer >

Mark the Correct alternative in the following:

If , then

view answer >