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

Chapter 4 Selina Maths Solution for ICSE Class 10th

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)

Note:- Before viewing Solution of Chapter-4 Linear Equations in One Variable of Concise Solution read the Chapter Carefully then solve all example of your text book. The Chapter Chapter-4 Linear Equations in One Variable is important Chapter in ICSE board.

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

 

Question 1

State, true or false:

Ans 1 Exe 4 (a) Concise

Answer 1

Ans 1(i) Exe 4(a) Concise

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.

Answer 2

(i) a < ba – 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

Answer 3

(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

Answer 4

(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.

Answer 5

3 – 2x x – 12

-2x – x  -12 – 3

-3x -15

x5

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.

Answer 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:

Ans 3 Exe 4(a) Concise

Answer 7

Ans 7 (I) Exe 4(a)

Since, the replacement set of real numbers.Solution set = {x: x R and}

Ans 7 (ii) Exe 4(a) Concise

Since, the replacement set of real numbers.Solution set = { x: x R and }

Ans 7 (iii) Exe 4(a) Concise

Since, the replacement set of real numbers.Solution set = { x: x R and x > 80}

Ans 7 (iv) Exe 4(a) Concise

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.

Answer 8

Ans 8 Exe 4(a) Concise

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.

Answer 9

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.

Answer 10

Ans 10 Exe 4 (a) Concise

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

Question 11

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

Answer 11

Ans 11 Exe 4 (a) Concise

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

Question 12

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

.

Answer 12

Ans 20 Exe 4(a) Concise

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:

Que 1 Exe 4(b) Concise

Answer 1

Ans 1 Exe 4(b) Concise

Solution on number line is:

Ans 1(i) Exe 4 (b) Concise

Ans 1 (i) Exe 4(b) Concise

Question 2

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

Que 2 Exe 4(b) Concise

Answer 2

Ans 2 Exe4(b) Concise

Question 3

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

Que 3 Exe4(b) Concise

Question 4

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

Que 4(i) Exe 4(b) Concise

Ans 4(ii) Exe4(b) Concise

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.

Answer 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:

Ans 5 Exe 4(b) Concise

Question 6

List the elements of the solution set of the in equation

-3 < x – 2 ≤ 9 – 2x; x  N.

Answer 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.

Answer 7

Ans 7 Exe 4 (b) Concise

Question 8

Find the values of x, which satisfy the in equation:

Graph the solution on the number line.

Answer 8

Ans 8 Exe 4(b) Concise

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.

Answer 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.

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

2x – 3 < x + 2  ≤ 3x + 5, x  € R.

Answer 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}

Ans 11 Exe 4(b) Concise

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

Answer 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:

(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

Answer 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:

Ans 13 Exe 4(b) Concise

Question 14

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

Ans 14 Exe(b) Concise

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

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

Answer 14

(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:

Ans 15 Exe4(b) Concise

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

Answer 15

Ans 15 Exe 4(b) Concise Math

Question 16

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

Answer 16

Ans 16 Exe 4(b) Concise

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

Answer  17

Ans 17 Exe4(b) Concise

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.

Answer 18

Ans 18 Exe4(b) Concise

Question 19

Find the range of values of x, which satisfy:

Que 19 Exe4(b) Concise

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

Answer 19

Ans 19 Exe 4(b) Concise

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.

Answer 20

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

Answer 21

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:

Answer 22

Ans 22 Exe 4(b) Concise

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.

Answer 23

Ans 23 Exe4(b) Concise

Question 24

Find the set of values of x, satisfying:

7x + 3 ≥ 3x – 5 and   , where x  N.

Answer 24

Ans 24 Exe4(b) Concise

Question 25

Solve:

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

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

Answer 25

Ans 25 Exe4(b) Concise

Question 26

Solve the inequation:

  , x W. Graph the solution set on the number line.

Answer 26

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.

Answer 27

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.

Answer 28

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.

Answer 29

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:

Ans 29 Exe4(b) Concise

Question 30

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

Ans 30 Exe 4(b) Concise

Answer 30

Ans 30i Exe 4(b) Concise

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:Que 31 Exe 4(b) Concise

Answer 31

Consider the given in  equation:

Ans 32 Exe4(b) Concise

Question 32

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

Answer 32

Ans 33 Exe 4(b) Concise

Question 33

Que 33 Exe 4(b) Concise

Answer 33

Ans 33(I) Exe 4(n) Concise

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.

Answer 34

Ans 34 Exe 4(b) Concise

Question 35

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

Answer 35

Ans 35 Exe4(b) Concise

Question 36

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

Ans 36 Exe 4(b) Concise

Answer 36

Ans 36 (i) Exe 4(b) Concise

—–:End of Concise Solution Linear in Equations in One Variable Chapter 4 ICSE Class 10 :——

 

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