Concise Solution Linear in Equations in One Variable Chapter 4 ICSE Class 10. This post is Solution of Chapter 4 – Linear Equations in One Variable of  Concise Mathematics which is very famous Maths writer in ICSE Board in Maths Publication .Step by Step Concise Solution Chapter 4 – Linear Equations in One Variable is given to understand the topic clearly . Chapter Wise Solution of  Concise Solution including  Chapter 4 – Linear Equations in One Variable is very help full for ICSE Class 10th student appearing in 2020 exam of council.

## Concise Solution Linear in Equations in One Variable Chapter 4 ICSE Class 10

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### Exercise – 4(A) ,      Exercise – 4(B)

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### Exercise 4-(A) of  Concise Solution Linear in Equations in One Variable Chapter 4

#### Question 1

State, true or false:

#### 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 c0.

(i) a < b a – c < b – c

The given statement is true.

(ii) If a > ba + 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 + 32x + 18

(ii) 3x – 2 < 19 – 4x

(i) 5x + 3 2x + 18

5x – 2x 18 – 3

3x 15

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 11

(ii) 3x – 1 > 8

(iii) 8 – x > 5

(iv) 7 – 3x (v) (vi) 18  3x – 2

(i) x + 7 11

x 11 – 7

x 4

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

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

(ii) 3x – 1 > 8

3x > 8 + 1

x > 3

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

Solution set = {4, 5, 6, …}

(iii) 8 – x > 5

– x > 5 – 8

– x > -3

x < 3

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

Solution set = {0, 1, 2}

(iv) 7 – 3x -3x -7

-3x  Since, the replacement set = W (set of whole numbers)

Solution set = {0, 1, 2}

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

Solution set = {0, 1}

(vi) 18 3x – 2

18 + 2   3x

20 3x

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

Solution set = {7, 8, 9, …}

#### Question 5

Solve the inequation:

3 – 2x     x – 12 given that x N.

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.

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:

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 <      , where x is an integer.

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

#### Question 9

Find the largest value of x for which

2(x – 1) ≤ 9 – x and x W.

2(x – 1) ≤9 – x

2x – 2 ≤  9 – x

2x + x  ≤ 9 + 2

3x  ≤11

Since, x W, thus the required largest value of x is 3.

#### Question 10

Solve the in equation:   and x   R.

Solution set = {x: x R and x 6}

#### Question 11

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

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

#### Question 12

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

.

Since, x  {whole numbers}Solution set = {0, 1, 2, 3, 4}

### Chapter 4 – Linear in Equations in One Variable Exercise-4(B) Concise Selina Solution

#### Question 1

Represent the following inequalities on real number lines:

Solution on number line is:

#### Question 2

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

#### Question 3

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

#### Question 4

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

The solution on number line is: #### Question 5

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

-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 in equation

-3 < x – 2 ≤ 9 – 2x; x N.

-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.

#### Question 8

Find the values of x, which satisfy the in equation: Graph the solution on the number line.

#### 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.

-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.

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 in equation and graph the solution set on the number line:

2x – 3 < x + 2  ≤ 3x + 5, x  € R.

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}

#### 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

(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:

(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

(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:

#### Question 14

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

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

(ii) Represent A  B and A  B’ on two different number lines.

(i) A = {x  R: -2 x < 5}

B = {x  R: -4 x < 3}

(ii) A  B = {x  R: -2  x < 5}

It can be represented on number line as:

#### 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

#### Question 16

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

#### Question 17

Given A = {x: -1 < x ≤ 5, x  ≤R} and B = {x: -4  x < 3, x ≤ R}

Represent on different number lines:

(i) A ∩ B

(ii) A’ ∩ B

(iii) A – B

#### Question 18

P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45  5(x – 5); where x  R. Represent:

(i) P Q

(ii) P – Q

(iii) PQ’

on different number lines.

#### Question 19

Find the range of values of x, which satisfy:

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

(i) x  W (ii) x  Z (iii) x  R

#### Question 20

Given: A = {x: -8 < 5x + 2 ≤ 17, x € I}, B = {x: -2 ≤ 7 + 3x < 17, x € R}

Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A ∩ B.

A = {x: -8 < 5x + 2 ≤ 17, x€  I}

= {x: -10 < 5x ≤ 15, x € I}

= {x: -2 < x ≤ 3, x € I}

It can be represented on number line as follows: B = {x: -2 ≤ 7 + 3x < 17, x € R}

= {x: -9 ≤ 3x < 10, x € R}

= {x: -3 ≤ x < 3.33, x € R}

It can be represented on number line as follows:

A B = {-1, 0, 1, 2, 3}

#### Question 21

Solve the following inequation and represent the solution set on the number line 2x – 5 ≤ 5x +4 < 11, where x  I

2x – 5 ≤ 5x +4 and 5x +4 < 11

2x – 5x ≤ 4 – 5 and 5x < 11 – 4

3x ≤ – 1 and 5x < 7

x ≥ – 1 and x < x ≥ – 1 and x <

Since x I, the solution set is And the number line representation is

#### Question 22

Given that x € I, solve the in equation and graph the solution on the number line: #### Question 23

Given:

A = {x: 11x – 5 > 7x + 3, x € R} and

B = {x: 18x – 9  15 + 12x, x € R}.

Find the range of set A ∩ B and represent it on number line.

#### Question 24

Find the set of values of x, satisfying:

7x + 3 ≥ 3x – 5 and , where x  N.

#### Question 25

Solve:

(i) , where x is a positive odd integer.

(ii)     , where x is a positive even integer.

#### Question 26

Solve the inequation: , x W. Graph the solution set on the number line.

Since, x € W

Solution set = {0, 1, 2}

The solution set can be represented on number line as: #### Question 27

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 at most 20.

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 28

Solve the given in equation and graph the solution on the number line. 2y – 3 < y + 1  ≤ 4y + 7, y R

2y – 3 – y < y + 1 – y ≤ 4y + 7 – y

y – 3 < 1 ≤ 3y + 7

y – 3 < 1 and 1 ≤3y + 7

y < 4 and 3y ≥ – 6  ⇒y ≥ – 2

– 2 ≤ y < 4

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

#### Question 29

Solve the inequation:

3z – 5 ≤ z + 3 < 5z – 9, z  R.

Graph the solution set on the number line.

3z – 5 ≤ z + 3 < 5z – 9

3z – 5 ≤ z + 3 and z + 3 < 5z – 9

2z ≤ 8 and 12 < 4z

z ≤ 4 and 3 < z

Since, z € R

Solution set = {3 < z  4, Z  R }

It can be represented on a number line as:

#### Question 30

Solve the following in equation and represent the solution set on the number line.

The solution set can be represented on a number line as: #### Question 31

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

Consider the given in  equation:

#### Question 32

Solve the following in equation, write the solution set and represent it on the number line: #### Question 34

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.

#### Question 35

Solve the following in equation, write the solution set and represent it on the number line. #### Question 36

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