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

## Chapter 8: Linear Inequations

Exercise 8.1Exercise 8.2Exercise 8.3Miscellaneous Exercise 8
Exercise 8.1 [Page 116]

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

Exercise 8.1 | Q 1. (i) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
[−4, 7/3]

Exercise 8.1 | Q 1. (ii) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
[0, 0.9]

Exercise 8.1 | Q 1. (iii) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
(- ∞,∞)

Exercise 8.1 | Q 1. (iv) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
[5, ∞]

Exercise 8.1 | Q 1. (v) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
(– 11, – 2)

Exercise 8.1 | Q 1. (vi) | Page 116

Write the inequation that represent the interval and state whether the interval is bounded or unbounded.
(-∞, 3)

Exercise 8.1 | Q 2. (i) | Page 116

Solve the following inequation: 3x – 36 > 0

Exercise 8.1 | Q 2. (ii) | Page 116

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

Exercise 8.1 | Q 2. (iii) | Page 116

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

Exercise 8.1 | Q 2. (iv) | Page 116

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

Exercise 8.1 | Q 3. (i) | Page 116

Sketch the graph which represents the solution set for the following inequation.
x > 5

Exercise 8.1 | Q 3. (ii) | Page 116

Sketch the graph which represents the solution set for the following inequation.
x ≥ 5

Exercise 8.1 | Q 3. (iii) | Page 116

Sketch the graph which represents the solution set for the following inequation.
x < 3

Exercise 8.1 | Q 3. (iv) | Page 116

Sketch the graph which represents the solution set for the following inequation.
x ≤ 3

Exercise 8.1 | Q 3. (v) | Page 116

Sketch the graph which represents the solution set for the following inequation.
– 4 < x < 3

Exercise 8.1 | Q 3. (vi) | Page 116

Sketch the graph which represents the solution set for the following inequation.
– 2 ≤ x < 2.5

Exercise 8.1 | Q 3. (vii) | Page 116

Sketch the graph which represents the solution set for the following inequation.
– 3 ≤ x ≤ 1

Exercise 8.1 | Q 3. (viii) | Page 116

Sketch the graph which represents the solution set for the following inequation.
|x| < 4

Exercise 8.1 | Q 3. (ix) | Page 116

Sketch the graph which represents the solution set for the following inequation.
|x| ≥ 3.5

Exercise 8.1 | Q 4. (i) | Page 116

Solve the inequation:
5x + 7 > 4 – 2x

Exercise 8.1 | Q 4. (ii) | Page 116

Solve the inequation:
3x + 1 ≥ 6x – 4

Exercise 8.1 | Q 4. (iii) | Page 116

Solve the inequation:
4 – 2x < 3(3 – x)

Exercise 8.1 | Q 4. (iv) | Page 116

Solve the inequation:
3/4 "x" - 6 ≤ "x" - 7

Exercise 8.1 | Q 4. (v) | Page 116

Solve the inequation:
– 8 ≤ – (3x – 5) < 13

Exercise 8.1 | Q 4. (vi) | Page 116

Solve the inequation:
– 1 < 3  – "x"/5 ≤ 1

Exercise 8.1 | Q 4. (vii) | Page 116

Solve the inequation:
2|4 – 5x| ≥ 9

Exercise 8.1 | Q 4. (viii) | Page 116

Solve the inequation:
|2x + 7| ≤ 25

Exercise 8.1 | Q 4. (ix) | Page 116

Solve the inequation:
2|x + 3| > 1

Exercise 8.1 | Q 4. (x) | Page 116

Solve the inequation:
("x" + 5)/("x" - 3) < 0

Exercise 8.1 | Q 4. (xi) | Page 116

Solve the inequation:
("x" - 2)/("x" + 5) > 0

Exercise 8.1 | Q 5 | Page 116

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.

Exercise 8.1 | Q 6 | Page 116

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.

Exercise 8.1 | Q 7 | Page 116

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

Exercise 8.1 | Q 8 | Page 116

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

Exercise 8.1 | Q 9 | Page 116

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.

Exercise 8.2 [Page 120]

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

Exercise 8.2 | Q 1. (i) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
x ≤ – 4

Exercise 8.2 | Q 1. (ii) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
y ≥ 3

Exercise 8.2 | Q 1. (iii) | Page 120

Solve the following inequations graphically in two-dimensional plane.
y ≤ – 2x

Exercise 8.2 | Q 1. (iv) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
y – 5x ≥ 0

Exercise 8.2 | Q 1. (v) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
x – y ≥ 0

Exercise 8.2 | Q 1. (vi) | Page 120

Solve the following inequation graphically in two-dimensional plane.
2x – y ≤ − 2

Exercise 8.2 | Q 1. (vii) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
4x + 5y ≤  40

Exercise 8.2 | Q 1. (viii) | Page 120

Solve the following inequation graphically in the two-dimensional plane.
1/4 "x" + 1/2 "y" ≤ 1

Exercise 8.2 | Q 2 | Page 120

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.

Exercise 8.2 | Q 3 | Page 120

Diet of a sick person must contain at least 4000 units of vitamin. Each unit of food F1 contains 200 units of vitamin, where as each unit of food F2 contains 100 units of vitamins. Write an inequation to fulfil sick person’s requirements and  represent the solution set graphically.

Exercise 8.3 [Page 121]

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

Exercise 8.3 | Q 1 | Page 121

Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2

Exercise 8.3 | Q 2 | Page 121

Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3

Exercise 8.3 | Q 3 | Page 121

Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400

Exercise 8.3 | Q 4 | Page 121

Find the graphical solution of the following system of linear inequations:
0 ≤ x ≤ 350, 0 ≤ y ≤ 150

Exercise 8.3 | Q 5 | Page 121

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

Exercise 8.3 | Q 6 | Page 121

Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 24, 3x + y ≥ 15, x ≥ 4

Exercise 8.3 | Q 7 | Page 121

Find the graphical solution of the following system of linear inequations:
2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0

Miscellaneous Exercise 8 [Page 122]

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

Miscellaneous Exercise 8 | Q 1 | Page 122

Solve the following system of inequalities graphically.
x ≥ 3, y ≥ 2

Miscellaneous Exercise 8 | Q 2 | Page 122

Solve the following system of inequalities graphically.
3x + 2y ≤ 12, x ≥ 1, y ≥ 2

Miscellaneous Exercise 8 | Q 3 | Page 122

Solve the following system of inequalities graphically.
2x + y ≥ 6, 3x + 4y ≤ 12

Miscellaneous Exercise 8 | Q 4 | Page 122

Solve the following system of inequalities graphically.
x + y ≥ 4, 2x – y ≤ 0

Miscellaneous Exercise 8 | Q 5 | Page 122

Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1

Miscellaneous Exercise 8 | Q 6 | Page 122

Solve the following system of inequalities graphically.
x + y ≤ 6, x + y ≥ 4

Miscellaneous Exercise 8 | Q 7 | Page 122

Solve the following system of inequalities graphically.
2x + y ≥ 8, x + 2y ≥ 10

Miscellaneous Exercise 8 | Q 8 | Page 122

Solve the following system of inequalities graphically.
x + y ≤ 9, y > x, x ≥ 0

Miscellaneous Exercise 8 | Q 9 | Page 122

Solve the following system of inequalities graphically.
5x + 4y ≤ 20, x ≥ 1, y ≥ 2

Miscellaneous Exercise 8 | Q 10 | Page 122

Solve the following system of inequalities graphically.
3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0

Miscellaneous Exercise 8 | Q 11 | Page 122

Solve the following system of inequalities graphically.
2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6

Miscellaneous Exercise 8 | Q 12 | Page 122

Solve the following system of inequalities graphically.
x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

Miscellaneous Exercise 8 | Q 13 | Page 122

Solve the following system of inequalities graphically.
4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

Miscellaneous Exercise 8 | Q 14 | Page 122

Solve the following system of inequalities graphically.
3x + 2y ≤ 150, x + 4y ≥ 80, x ≤ 15, y ≥ 0, x ≥ 0

Miscellaneous Exercise 8 | Q 15 | Page 122

Solve the following system of inequalities graphically.
x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0

## Chapter 8: Linear Inequations

Exercise 8.1Exercise 8.2Exercise 8.3Miscellaneous Exercise 8

## 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.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using Balbharati 11th solutions Linear Inequations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 11th prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 8 Linear Inequations 11th extra questions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation