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NCERT solutions Mathematics Textbook for Class 11 chapter 6 Linear Inequalities

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Chapter 6 - Linear Inequalities

Pages 122 - 123

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

Q 1.1 | Page 122 | view solution

Solve 24x < 100, when x is an integer

Q 1.2 | Page 122 | view solution

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

Q 2.1 | Page 122 | view solution

Solve –12x > 30, when x is an integer

Q 2.2 | Page 122 | view solution

Solve 5x– 3 < 7, when x is an integer

Q 3.1 | Page 122 | view solution

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

Q 3.2 | Page 122 | view solution

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

Q 4.1 | Page 122 | view solution

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

Q 4.2 | Page 122 | view solution

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

Q 5 | Page 122 | view solution

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

Q 6 | Page 122 | view solution

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

Q 7 | Page 122 | view solution

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

Q 8 | Page 122 | view solution

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

Q 9 | Page 122 | view solution

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

Q 10 | Page 122 | view solution

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

Q 11 | Page 122 | view solution

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

Q 11 | Page 122 | view solution

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

Q 12 | Page 122 | view solution

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

Q 13 | Page 122 | view solution

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

Q 14 | Page 122 | view solution

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

Q 15 | Page 122 | view solution

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

Q 16 | Page 122 | view solution

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

Q 17 | Page 122 | view solution

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

Q 18 | Page 122 | view solution

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

Q 19 | Page 122 | view solution

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

Q 20 | Page 122 | view solution

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.

Q 21 | Page 122 | view solution

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.

Q 22 | Page 122 | view solution

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

Q 23 | Page 122 | view solution

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

Q 24 | Page 122 | view solution

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.

Q 25 | Page 123 | view solution

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 2x are the lengths of the second and third piece, respectively. Thus, x = (+ 3) + 2≤ 91 and 2x ≥ (+ 3) + 5]

Q 26 | Page 123 | view solution

Page 127

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

Q 1 | Page 127 | view solution

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

Q 2 | Page 127 | view solution

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

Q 3 | Page 127 | view solution

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

Q 4 | Page 127 | view solution

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

Q 5 | Page 127 | view solution

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

Q 6 | Page 127 | view solution

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

Q 6.2 | Page 127 | view solution

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

Q 7 | Page 127 | view solution

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

Q 8 | Page 127 | view solution

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

Q 9 | Page 127 | view solution

Page 129

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

Q 1 | Page 129 | view solution

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

Q 2 | Page 129 | view solution

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

Q 3 | Page 129 | view solution

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

Q 4 | Page 129 | view solution

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

Q 5 | Page 129 | view solution

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

Q 6 | Page 129 | view solution

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

Q 7 | Page 129 | view solution

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

Q 8 | Page 129 | view solution

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

Q 9 | Page 129 | view solution

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

Q 10 | Page 129 | view solution

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

Q 11 | Page 129 | view solution

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

Q 12 | Page 129 | view solution

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

Q 13 | Page 129 | view solution

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

Q 14 | Page 129 | view solution

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

Q 15 | Page 129 | view solution

Page 132

Solve the inequality 2 ≤ 3x – 4 ≤ 5

Q 1 | Page 132 | view solution

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

Q 2 | Page 132 | view solution

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

Q 3 | Page 132 | view solution

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

Q 4 | Page 132 | view solution

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

Q 5 | Page 132 | view solution

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

Q 6 | Page 132 | view solution

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

Q 7 | Page 132 | view solution

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

Q 8 | Page 132 | view solution

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

3x – 7 > 2(x – 6), 6 – x > 11 – 2x

Q 9 | Page 132 | view solution

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

Q 10 | Page 132 | view solution

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 ?

Q 11 | Page 132 | view solution

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?

Q 12 | Page 132 | view solution

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?

Q 13 | Page 132 | view solution

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.

Q 14 | Page 132 | view solution

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