#### Chapters

## Chapter 8: Linear Inequations

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 8 Linear Inequations Exercise 8.1 [Page 116]

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

[−4, 7/3]

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

[0, 0.9]

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

`(- ∞,∞)`

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

`[5, ∞]`

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

(– 11, – 2)

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.

`(-∞, 3)`

Solve the following inequation: 3x – 36 > 0

Solve the following inequation: 7x – 25 ≤ – 4

Solve the following inequation: `0 < ("x" - 5)/4 < 3`

Solve the following inequation: |7x – 4| < 10

Sketch the graph which represents the solution set for the following inequation.

x > 5

Sketch the graph which represents the solution set for the following inequation.

x ≥ 5

Sketch the graph which represents the solution set for the following inequation.

x < 3

Sketch the graph which represents the solution set for the following inequation.

x ≤ 3

Sketch the graph which represents the solution set for the following inequation.

– 4 < x < 3

Sketch the graph which represents the solution set for the following inequation.

– 2 ≤ x < 2.5

Sketch the graph which represents the solution set for the following inequation.

– 3 ≤ x ≤ 1

Sketch the graph which represents the solution set for the following inequation.

|x| < 4

Sketch the graph which represents the solution set for the following inequation.

|x| ≥ 3.5

Solve the inequation:

5x + 7 > 4 – 2x

Solve the inequation:

3x + 1 ≥ 6x – 4

Solve the inequation:

4 – 2x < 3(3 – x)

Solve the inequation:

`3/4 "x" - 6 ≤ "x" - 7`

Solve the inequation:

– 8 ≤ – (3x – 5) < 13

Solve the inequation:

`– 1 < 3 – "x"/5 ≤ 1`

Solve the inequation:

2|4 – 5x| ≥ 9

Solve the inequation:

|2x + 7| ≤ 25

Solve the inequation:

2|x + 3| > 1

Solve the inequation:

`("x" + 5)/("x" - 3) < 0`

Solve the inequation:

`("x" - 2)/("x" + 5) > 0`

Rajiv obtained 70 and 75 marks in first two unit tests. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94, and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.

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

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

The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm then find the minimum length of the shortest side.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 8 Linear Inequations Exercise 8.2 [Page 120]

Solve the following inequation graphically in the two-dimensional plane.

x ≤ – 4

Solve the following inequation graphically in the two-dimensional plane.

y ≥ 3

Solve the following inequations graphically in two-dimensional plane.

y ≤ – 2x

Solve the following inequation graphically in the two-dimensional plane.

y – 5x ≥ 0

Solve the following inequation graphically in the two-dimensional plane.

x – y ≥ 0

Solve the following inequation graphically in two-dimensional plane.

2x – y ≤ − 2

Solve the following inequation graphically in the two-dimensional plane.

4x + 5y ≤ 40

Solve the following inequation graphically in the two-dimensional plane.

`1/4 "x" + 1/2 "y" ≤ 1`

Mr. Rajesh. Has Rs. 1800 to spend on fruits for a meeting. Grapes cost Rs. 150 per kg. and peaches cost Rs. 200 per kg. Formulate and solve it graphically.

Diet of a sick person must contain at least 4000 units of vitamin. Each unit of food F_{1} contains 200 units of vitamin, where as each unit of food F_{2} contains 100 units of vitamins. Write an inequation to fulfil sick person’s requirements and represent the solution set graphically.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 8 Linear Inequations Exercise 8.3 [Page 121]

Find the graphical solution of the following system of linear inequations:

x – y ≤ 0, 2x – y ≥ − 2

Find the graphical solution of the following system of linear inequations:

2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3

Find the graphical solution of the following system of linear inequations:

3x + 2y ≤ 1800, 2x + 7y ≤ 1400

Find the graphical solution of the following system of linear inequations:

0 ≤ x ≤ 350, 0 ≤ y ≤ 150

Find the graphical solution of the following system of linear inequations:

`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0

Find the graphical solution of the following system of linear inequations:

3x + 2y ≤ 24, 3x + y ≥ 15, x ≥ 4

Find the graphical solution of the following system of linear inequations:

2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 8 Linear Inequations Miscellaneous Exercise 8 [Page 122]

Solve the following system of inequalities graphically.

x ≥ 3, y ≥ 2

Solve the following system of inequalities graphically.

3x + 2y ≤ 12, x ≥ 1, y ≥ 2

Solve the following system of inequalities graphically.

2x + y ≥ 6, 3x + 4y ≤ 12

Solve the following system of inequalities graphically.

x + y ≥ 4, 2x – y ≤ 0

Solve the following system of inequalities graphically.

2x – y ≥ 1, x – 2y ≤ – 1

Solve the following system of inequalities graphically.

x + y ≤ 6, x + y ≥ 4

Solve the following system of inequalities graphically.

2x + y ≥ 8, x + 2y ≥ 10

Solve the following system of inequalities graphically.

x + y ≤ 9, y > x, x ≥ 0

Solve the following system of inequalities graphically.

5x + 4y ≤ 20, x ≥ 1, y ≥ 2

Solve the following system of inequalities graphically.

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

Solve the following system of inequalities graphically.

2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6

Solve the following system of inequalities graphically.

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

Solve the following system of inequalities graphically.

4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

Solve the following system of inequalities graphically.

3x + 2y ≤ 150, x + 4y ≥ 80, x ≤ 15, y ≥ 0, x ≥ 0

Solve the following system of inequalities graphically.

x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0

## Chapter 8: Linear Inequations

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 8 - Linear Inequations

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 8 (Linear Inequations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 8 Linear Inequations are Linear Inequality, Solution of Linear Inequality, Graphical Representation of Solution of Linear Inequality in One Variable, Graphical Solution of Linear Inequality of Two Variable, Solution of System of Linear Inequalities in Two Variables.

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