#### Chapters

Chapter 2 - Relations and Functions

Chapter 3 - Trigonometric Functions

Chapter 4 - Principle of Mathematical Induction

Chapter 5 - Complex Numbers and Quadratic Equations

Chapter 6 - Linear Inequalities

Chapter 7 - Permutations and Combinations

Chapter 8 - Binomial Theorem

Chapter 9 - Sequences and Series

Chapter 10 - Straight Lines

Chapter 11 - Conic Sections

Chapter 12 - Introduction to Three Dimensional Geometry

Chapter 13 - Limits and Derivatives

Chapter 14 - Mathematical Reasoning

Chapter 15 - Statistics

Chapter 16 - Probability

## Chapter 6 - Linear Inequalities

#### Pages 122 - 123

Solve 24*x* < 100, when *x* is a natural number

Solve 24*x* < 100, when *x* is an integer

Solve –12*x* > 30, when *x* is a natural number

Solve –12*x* > 30, when *x* is an integer

Solve 5*x*– 3 < 7, when *x* is an integer

Solve 5*x*– 3 < 7, when *x* is a real number

Solve 3*x* + 8 > 2, when *x* is an integer

Solve 3*x* + 8 > 2, when *x* is a real number

Solve the given inequality for real *x*: 4*x* + 3 < 5*x* + 7

Solve the given inequality for real *x*: 3*x* – 7 > 5*x* – 1

Solve the given inequality for real *x*: 3(*x* – 1) ≤ 2 (*x *– 3)

Solve the given inequality for real *x*: 3(2 – *x*) ≥ 2(1 – *x*)

Solve the given inequality for real *x : *x+ `x/2` + `x/3` < 11`

Solve the given inequality for real *x : `x/3 > x/2 + 1`*

Solve the given inequality for real x : `(3(x-2))/5 <= (5(2-x))/3`

Solve the given inequality for real x : `(3(x-2))/5 <= (5(2-x))/3`

Solve the given inequality for real *x*: `1/2 (3x/5 + 4) >= 1/3 (x -6)`

Solve the given inequality for real *x*: 2(2*x* + 3) – 10 < 6 (*x* – 2)

Solve the given inequality for real *x*: 37 – (3*x* + 5) ≥ 9*x* – 8(*x *– 3)

Solve the given inequality for real *x: *`x/4 < (5x - 2)/3 - (7x - 3)/5`

Solve the given inequality for real *x*: `(2x- 1)/3 >= (3x - 2)/4 - (2-x)/5`

Solve the given inequality and show the graph of the solution on number line: 3*x* – 2 < 2*x* +1

Solve the given inequality and show the graph of the solution on number line: 5*x* – 3 ≥ 3*x* – 5

Solve the given inequality and show the graph of the solution on number line: 3(1 – *x*) < 2 (*x* + 4)

Solve the given inequality and show the graph of the solution on number line `x/2 >= (5x -2)/3 - (7x - 3)/5`

Ravi obtained 70 and 75 marks in first two unit test. 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 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

[Hint: If *x* is the length of the shortest board, then *x*, (*x* + 3) and 2*x* are the lengths of the second and third piece, respectively. Thus, *x* = (*x *+ 3) + 2*x *≤ 91 and 2*x* ≥ (*x *+ 3) + 5]

#### Page 127

Solve the given inequality graphically in two-dimensional plane: *x* + *y* < 5

Solve the given inequality graphically in two-dimensional plane: 2*x* + *y* ≥ 6

Solve the given inequality graphically in two-dimensional plane: 3*x* + 4*y* ≤ 12

Solve the given inequality graphically in two-dimensional plane: *y* + 8 ≥ 2*x*

Solve the given inequality graphically in two-dimensional plane: *x* – *y* ≤ 2

Solve the given inequality graphically in two-dimensional plane: 2*x* – 3*y* > 6

Solve the given inequality graphically in two-dimensional plane: *x* > –3

Solve the given inequality graphically in two-dimensional plane: –3*x* + 2*y* ≥ –6

Solve the given inequality graphically in two-dimensional plane: 3*y* – 5*x* < 30

Solve the given inequality graphically in two-dimensional plane: *y* < –2

#### Page 129

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

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

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

Solve the following system of inequalities graphically: *x* + *y*≥ 4, 2*x* – *y* > 0

Solve the following system of inequalities graphically: 2*x* – *y* > 1, *x* – 2*y* < –1

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

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

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

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

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

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

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

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

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

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

#### Page 132

Solve the inequality 2 ≤ 3*x* – 4 ≤ 5

Solve the inequality 6 ≤ –3(2*x* – 4) < 12

Solve the inequality `-3 <= 4 - (7x)/2 < = 18`

Solve the inequality `-15 < (3(x - 2))/5 <= 0`

Solve the inequality `-12 < 4 - (3x)/(-5) <= 2`

Solve the inequality `7 <= (3x + 11)/2 <= 11`

Solve the inequalities and represent the solution graphically on number line: 5*x* + 1 > –24, 5*x* – 1 < 24

Solve the inequalities and represent the solution graphically on number line: 2(*x* – 1) < *x* + 5, 3(*x* + 2) > 2 – *x*

Solve the following inequalities and represent the solution graphically on number line:

3*x* – 7 > 2(*x* – 6), 6 – *x* > 11 – 2*x*

Solve the inequalities and represent the solution graphically on number line: 5(2*x* – 7) – 3(2*x* + 3) ≤ 0, 2*x* + 19 ≤ 6*x* + 47

A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by `F= 9/8` C + 32 ?

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 we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

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

IQ of a person is given by the formula

IQ = `(MA)/(CA) xx100`

Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

#### Textbook solutions for Class 11

## NCERT solutions for Class 11 Mathematics chapter 6 - Linear Inequalities

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Concepts covered in Class 11 Mathematics chapter 6 Linear Inequalities are Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation, Graphical Solution of Linear Inequalities in Two Variables, Solution of System of Linear Inequalities in Two Variables, Inequalities - Introduction.

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