SELINA Solutions for Class 10 Maths Chapter 4 - Linear Inequations (in one variable)

Revise Selina Solutions for ICSE Class 10 Mathematics Chapter 4 Linear Inequations (in One Variable) for exam preparation. Learn to solve linear inequations algebraically and graphically with the step-wise solutions created by Maths experts. These solutions are prepared according to the latest syllabus and exam guidelines.

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Chapter 4 - Linear Equations in One Variable Exercise Ex. 4(A)

Question 1

State, true or false:

Solution 1

Question 2

State, whether the following statements are true or false:

(i) a < b, then a - c < b - c

(ii) If a > b, then a + c > b + c

(iii) If a < b, then ac > bc

(iv) If a > b, then

(v) If a - c > b - d, then a + d > b + c

(vi) If a < b, and c > 0, then a - c > b - c

Where a, b, c and d are real numbers and c 0.

Solution 2

(i) a < b a - c < b - c

The given statement is true.

(ii) If a > b a + c > b + c

The given statement is true.

(iii) If a < b ac < bc

The given statement is false.

(iv) If a > b

The given statement is false.

(v) If a - c > b - d a + d > b + c

The given statement is true.

(vi) If a < b a - c < b - c (Since, c > 0)

The given statement is false.

Question 3

If x N, find the solution set of inequations.

(i) 5x + 3 2x + 18

(ii) 3x - 2 < 19 - 4x

Solution 3

(i) 5x + 3 2x + 18

5x - 2x 18 - 3

3x 15

x 5

Since, x N, therefore solution set is {1, 2, 3, 4, 5}.

(ii) 3x - 2 < 19 - 4x

3x + 4x < 19 + 2

7x < 21

x < 3

Since, x N, therefore solution set is {1, 2}.

Question 4

If the replacement set is the set of whole numbers, solve:

(i) x + 7 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 11

(ii) 3x - 1 > 8

(iii) 8 - x > 5

(iv) 7 - 3x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(vi) 18 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x - 2

Solution 4

(i) x + 7 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 11

x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 11 - 7

x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {0, 1, 2, 3, 4}

(ii) 3x - 1 > 8

3x > 8 + 1

x > 3

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {4, 5, 6, …}

(iii) 8 - x > 5

- x > 5 - 8

- x > -3

x < 3

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {0, 1, 2}

(iv) 7 - 3x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

-3x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 7

-3x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {0, 1, 2}

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {0, 1}

(vi) 18 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x - 2

18 + 2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x

20 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Since, the replacement set = W (set of whole numbers)

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {7, 8, 9, …}

Question 5

Solve the inequation:

3 - 2x x - 12 given that x N.

Solution 5

3 - 2x x - 12

-2x - x -12 - 3

-3x -15

x 5

Since, x N, therefore,

Solution set = {1, 2, 3, 4, 5}

Question 6

If 25 - 4x 16, find:

(i) the smallest value of x, when x is a real number,

(ii) the smallest value of x, when x is an integer.

Solution 6

25 - 4x 16

-4x 16 - 25

-4x -9

x

x

(i) The smallest value of x, when x is a real number, is 2.25.

(ii) The smallest value of x, when x is an integer, is 3.

Question 7

If the replacement set is the set of real numbers, solve:

Solution 7

Since, the replacement set of real numbers.

Solution set = {x: x R and }

Since, the replacement set of real numbers.

Solution set = { x: x R and }

Since, the replacement set of real numbers.

Solution set = { x: x R and x > 80}

Since, the replacement set of real numbers.

Solution set = { x: x R and x > 13}

Question 8

Find the smallest value of x for which 5 - 2x <Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable, where x is an integer.

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Thus, the required smallest value of x is -1.

Question 9

Find the largest value of x for which

2(x - 1) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 9 - x and x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable W.

Solution 9

2(x - 1) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 9 - x

2x - 2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 9 - x

2x + x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 9 + 2

3x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 11

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Since, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable W, thus the required largest value of x is 3.

Question 10

Solve the inequation: Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable and x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R.

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {x: x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R and x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 6}

Question 11

Given x {integers}, find the solution set of:

Solution 11

Since, x {integers}

Solution set = {-1, 0, 1, 2, 3, 4}

Question 12

Given x {whole numbers}, find the solution set of:

.

Solution 12

Since, x {whole numbers}

Solution set = {0, 1, 2, 3, 4}

Chapter 4 - Linear Equations in One Variable Exercise Ex. 4(B)

Question 1

Represent the following inequalities on real number lines:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution on number line is:

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 2

For each graph given, write an inequation taking x as the variable:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 3

For the following inequations, graph the solution set on the real number line:

Solution 3

The solution set on the real number line is:

The solution set on the real number line is:

Question 4

Represent the solution of each of the following inequalities on the real number line:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable



The solution on number line is as follows:


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable



The solution on number line is as follows:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable



The solution on number line is as follows:


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable



The solution on number line is as follows:


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


The solution on number line is:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


The solution on number line is:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 5

x {real numbers} and -1 < 3 - 2x 7, evaluate x and represent it on a number line.

Solution 5

-1 < 3 - 2x 7

-1 < 3 - 2x and 3 - 2x 7

2x < 4 and -2x 4

x < 2 and x -2

Solution set = {-2 x < 2, x R}

Thus, the solution can be represented on a number line as:

Question 6

List the elements of the solution set of the inequation

-3 < x - 2 9 - 2x; x N.

Solution 6

-3 < x - 2 9 - 2x

-3 < x - 2 and x - 2 9 - 2x

-1 < x and 3x 11

-1 < x

Since, x N

Solution set = {1, 2, 3}

Question 7

Find the range of values of x which satisfies

Graph these values of x on the number line.

Solution 7

-3 x and x < 3

-3 x < 3

The required graph of the solution set is:

Question 8

Find the values of x, which satisfy the inequation:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Graph the solution on the number line. 

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Thus, the solution set is {x N: -2 ≤ x ≤3.75}

Since x N, the values of x are 1, 2, 3

The solution on number line is given by

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

Question 9

Given x {real numbers}, find the range of values of x for which -5 2x - 3 < x + 2 and represent it on a number line.

Solution 9

-5 2x - 3 < x + 2

-5 2x - 3 and 2x - 3 < x + 2

-2 2x and x < 5

-1 x and x < 5

Required range is -1 x < 5.

The required graph is:

Question 10

If 5x - 3 5 + 3x 4x + 2, express it as a x b and then state the values of a and b.

Solution 10

5x - 3 5 + 3x 4x + 2

5x - 3 5 + 3x and 5 + 3x 4x + 2

2x 8 and -x -3

x 4 and x 3

Thus, 3 x 4.

Hence, a = 3 and b = 4.

Question 11

Solve the following inequation and graph the solution set on the number line:

2x - 3 < x + 2 3x + 5, x R.

Solution 11

2x - 3 < x + 2 3x + 5

2x - 3 < x + 2 and x + 2 3x + 5

x < 5 and -3 2x

x < 5 and -1.5 x

Solution set = {-1.5 x < 5}

The solution set can be graphed on the number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 12

Solve and graph the solution set of:

(i) 2x - 9 < 7 and 3x + 9 25, x R

(ii) 2x - 9 7 and 3x + 9 > 25, x I

(iii) x + 5 4(x - 1) and 3 - 2x < -7, x R

Solution 12

(i) 2x - 9 < 7 and 3x + 9 25

2x < 16 and 3x 16

x < 8 and x 5

Solution set = { x 5, x R}

The required graph on number line is:

(ii) 2x - 9 7 and 3x + 9 > 25

2x 16 and 3x > 16

x 8 and x > 5

Solution set = {5 < x 8, x I} = {6, 7, 8}

The required graph on number line is:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(iii) x + 5 4(x - 1) and 3 - 2x < -7

9 3x and -2x < -10

3 x and x > 5

Solution set = Empty set

Question 13

Solve and graph the solution set of:

(i) 3x - 2 > 19 or 3 - 2x -7, x R

(ii) 5 > p - 1 > 2 or 7 2p - 1 17, p R

Solution 13

(i) 3x - 2 > 19 or 3 - 2x -7

3x > 21 or -2x -10

x > 7 or x 5

Graph of solution set of x > 7 or x 5 = Graph of points which belong to x > 7 or x 5 or both.

Thus, the graph of the solution set is:

(ii) 5 > p - 1 > 2 or 7 2p - 1 17

6 > p > 3 or 8 2p 18

6 > p > 3 or 4 p 9

Graph of solution set of 6 > p > 3 or 4 p 9

= Graph of points which belong to 6 > p > 3 or 4 p 9 or both

= Graph of points which belong to 3 < p 9

Thus, the graph of the solution set is:

Question 14

The diagram represents two inequations A and B on real number lines:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(i) Write down A and B in set builder notation.

(ii) Represent A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B and A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B' on two different number lines.

Solution 14

(i) A = {x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R: -2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 5}

 

B = {x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R: -4 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 3}

 

(ii) A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B = {x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R: -2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 5}

It can be represented on number line as:

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

B' = {x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R: 3 < x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable -4}

 

A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B' = {x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R: 3 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 5}

 

It can be represented on number line as:

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 15

Use real number line to find the range of values of x for which:

(i) x > 3 and 0 < x < 6

(ii) x < 0 and -3 x < 1

(iii) -1 < x 6 and -2 x 3

Solution 15

(i) x > 3 and 0 < x < 6

Both the given inequations are true in the range where their graphs on the real number lines overlap.

The graphs of the given inequations can be drawn as:

x > 3

0 < x < 6

From both graphs, it is clear that their common range is

3 < x < 6

(ii) x < 0 and -3 x < 1

Both the given inequations are true in the range where their graphs on the real number lines overlap.

The graphs of the given inequations can be drawn as:

x < 0

-3 x < 1

From both graphs, it is clear that their common range is

-3 x < 0

(iii) -1 < x 6 and -2 x 3

Both the given inequations are true in the range where their graphs on the real number lines overlap.

The graphs of the given inequations can be drawn as:

-1 < x 6

-2 x 3

From both graphs, it is clear that their common range is

-1 < x 3

Question 16

Illustrate the set {x: -3 x < 0 or x > 2, x R} on the real number line.

Solution 16

Graph of solution set of -3 x < 0 or x > 2

= Graph of points which belong to -3 x < 0 or x > 2 or both

Thus, the required graph is:

Question 17

Given A = {x: -1 < x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 5, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R} and B = {x: -4 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 3, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

Represent on different number lines:

(i) A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B

(ii) A' Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B

(iii) A - B

Solution 17

(i) A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B = {x: -1 < x < 3, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

It can be represented on a number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

(ii) Numbers which belong to B but do not belong to A' = B - A

A' Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B = {x: -4 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable -1, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

It can be represented on a number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

(iii) A - B = {x: 3 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 5, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

It can be represented on a number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 18

P is the solution set of 7x - 2 > 4x + 1 and Q is the solution set of 9x - 45 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 5(x - 5); where x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R. Represent:

(i) P Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Q

(ii) P - Q

(iii) P Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Q'

on different number lines.

Solution 18

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

and

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(ii) P - Q = {x: 1 < x < 5, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable{x: 1 < x < 5, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 20

Find the range of values of x, which satisfy:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Graph, in each of the following cases, the values of x on the different real number lines:

(i) x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable W (ii) x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Z (iii) x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R

Solution 20

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


(i)If x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable W, range of values of x is {0, 1, 2, 3, 4, 5, 6}.


 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


 

(ii) If x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable Z, range of values of x is {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}.


 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


 

(iii)If x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R, range of values of x is Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable.


 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Question 21

Given: A = {x: -8 < 5x + 2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 17, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable I}, B = {x: -2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 7 + 3x < 17, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B.

Solution 21

A = {x: -8 < 5x + 2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 17, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable I}

= {x: -10 < 5x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 15, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable I}

= {x: -2 < x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable I}

It can be represented on number line as follows:


 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


 

B = {x: -2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 7 + 3x < 17, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: -9 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x < 10, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: -3 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable x < 3.33, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

It can be represented on number line as follows:


Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B = {-1, 0, 1, 2, 3}

Question 22

Solve the following inequation and represent the solution set on the number line 2x - 5 ≤ 5x +4 < 11, where xSelina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableI

Solution 22

2x - 5 ≤ 5x + 4 and 5x +4 < 11

2x - 9 ≤ 5x  and 5x < 11 - 4

  -9 ≤ 3x and 5x < 7

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 3 and x < Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 3 and x < Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Since xSelina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable I, the solution set is Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

And the number line representation is

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 23

Given that x I, solve the inequation and graph the solution on the number line:

Solution 23

Solution set = {5, 6}

It can be graphed on number line as:

Question 24

Given:

A = {x: 11x - 5 > 7x + 3, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R} and

B = {x: 18x - 9 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 15 + 12x, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}.

Find the range of set A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B and represent it on number line.

Solution 24

A = {x: 11x - 5 > 7x + 3, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: 4x > 8, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: x > 2, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

B = {x: 18x - 9 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 15 + 12x, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: 6x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 24, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

= {x: x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

Range of A Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable B = {x: x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R}

It can be represented on number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 

Question 25

Find the set of values of x, satisfying:

7x + 3 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x - 5 and Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable, where x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable N.

Solution 25

7x + 3Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3x - 5

4x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable -8

x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable -2

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Since, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable N

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {1, 2, 3, 4, 5}

Question 26

Solve:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable, where x is a positive odd integer.

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable, where x is a positive even integer.

Solution 26

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Since, x is a positive odd integer

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {1, 3, 5}

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable


Since, x is a positive even integer

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {2, 4, 6, 8, 10, 12, 14}

Question 27

Solve the inequation:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableW. Graph the solution set on the number line.

Solution 27

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Since, x Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable W

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {0, 1, 2}

The solution set can be represented on number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 28

Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is atmost 20.

Solution 28

Let the required integers be x, x + 1 and x + 2.

According to the given statement,

Thus, the largest value of the positive integer x is 24.

Hence, the required integers are 24, 25 and 26.

Question 29

Solve the given inequation and graph the solution on the number line.

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 29

2y - 3 < y + 1 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4y + 7, y Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableR

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable2y - 3 - y < y + 1 - y Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4y + 7 - y

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable y - 3 < 1 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3y + 7

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable y - 3 < 1 and 1Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 3y + 7

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable y < 4 and 3y Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 6 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable y Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 2

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable - 2 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable y < 4

The graph of the given equation can be represented on a number line as:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 30

Solve the inequation:

3z - 5 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable z + 3 < 5z - 9, z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R.

Graph the solution set on the number line.

Solution 30

3z - 5 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable z + 3 < 5z - 9

3z - 5 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable z + 3 and z + 3 < 5z - 9

2z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 8 and 12 < 4z

z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4 and 3 < z

Since, z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One VariableSolution set = {3 < z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 4, Z Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable R }

It can be represented on a number line as:

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 31

Solve the following inequation and represent the solution set on the number line.

-3 < R

Solution 31

The solution set can be represented on a number line as:

Question 32

Solve the following inequation and represent the solution set on the number line:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 32

Consider the given inequation:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

-4 ≤ x < 5; where x  R

The solution set can be represented on a number line as follows:

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Question 33

Solve the following in equation, write the solution set and represent it on the number line:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 33

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

 

Question 34

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 34

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

 

Question 35

Solve the following in equation and write the solution set:

13x - 5 < 15x + 4 < 7x + 12, x R

Represent the solution on a real number line.

Solution 35

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

Question 36

Solve the following inequation, write the solution set and represent it on the number line.

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

Solution 36

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

 Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

The solution set is represented on number line as follows:

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable 

Question 37

Solve the following inequation and represent the solution set on a number line.

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Solution 37

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

As, Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable

Selina Solutions Icse Class 10 Mathematics Chapter - Linear Inequations In One Variable