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# Selina solutions for Class 10 Mathematics chapter 4 - Linear Inequations (In one variable)

## Chapter 4: Linear Inequations (In one variable)

4A4B

#### Chapter 4: Linear Inequations (In one variable) Exercise 4A solutions [Page 0]

State true or false

x < -y => -x > y

• True

• False

State true or false

-5x >= 15 => x >= -3

• True

• False

State true or false

2x <= -7 => (2x)/(-4) >= (-7)/(-4)

• True

• False

State true or false

7 > 5 => 1/7 < 1/5

• True

• False

State, whether the following statements are true or false:

a < b, then a – c < b – c

• True

• False

State, whether the following statements are true or false:

If a > b, then a + c > b + c

• True

• False

State, whether the following statements are true or false:

IF a < b, then ac < bc

• True

• False

State, whether the following statements are true or false:

if a > b then a/c > b/c

• True

• False

State, whether the following statements are true or false:

If a – c > b – d, then a + d > b + c

• True

• False

State, whether the following statements are true or false:

If a < b, and c > 0, then a – c < b – c
Where a, b, c and d are real numbers and c ≠ 0.

• True

• False

If x ∈ N, find the solution set of inequations.

5x + 3 ≤ 2x + 18

If x ∈ N, find the solution set of inequations.

3x – 2 < 19 – 4x

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

x + 7 <= 11

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

3x - 1 > 8

If the replacement set is the set of whole numbers solve

8 - x > 5

If the replacement set is the set of whole numbers solve

7 - 3x >= - 1/2

If the replacement set is the set of whole numbers solve

x  - 3/2 < 3/2 - x

If the replacement set is the set of whole numbers solve

18<= 3x - 2

Solve the inequation:

3 – 2x ≥ x – 12 given that x ∈ N.

If 25 – 4x ≤ 16, find:

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

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

If the replacement set is the set of real numbers solve

-4x >= - 16

If the replacement set is the set of real numbers solve

8 - 3x  <= 20

If the replacement set is the set of real numbers solve

5 + x/4 > x/5 + 9

If the replacement set is the set of real numbers solve

(x + 3)/8 < (x - 3)/5

Find the smallest value of x for which 5 - 2x < 5 1/2 - 5/3x where x  is interger

Find the largest value of x for which 2(x – 1) ≤ 9 – x and x ∈ W.

Solve the inequation 12 + 1 5/6 xx ≤ 5 + 3x and x in R

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

-5 ≤ 2x – 3 < x + 2

Given x ∈ {whole numbers}, find the solution set of: -1 ≤ 3 + 4x < 23

#### Chapter 4: Linear Inequations (In one variable) Exercise 4B solutions [Page 0]

Represent the following inequalities on real number lines

2x - 1 < 5

Represent the following inequalities on real number lines

3x + 1 >= -5

Represent the following inequalities on real number lines

2(2x- 3) <= 6

Represent the following inequalities on real number lines

-4 < x < 4

Represent the following inequalities on real number lines

-2 <= x  < 5

Represent the following inequalities on real number lines

8 >= x > -3

Represent the following in-equalities on real number line :

−5 < × ≤ −1

For graph given write an inequation taking x as the variable

For graph given write an inequation taking x as the variable

For graph given write an inequation taking x as the variable

For graph given write an inequation taking x as the variable

For the given inequations graph the solution set on the real number line

-4 < 3x - 1 < 8

For the given inequations graph the solution set on the real number line

x - 1 < 3 -  x <= 5

Represent the solution of the given inequalities on the real number line

4x - 1 > x + 11

Represent the solution of the given inequalities on the real number line

7 - x <= 2 - 6x

Represent the solution of the given inequalities on the real number line

x + 3 <= 2x + 9

Represent the solution of the given inequalities on the real number line

2 - 3x > 7 - 5x

Represent the solution of the given inequalities on the real number line

1 + x >= 5x - 11

Represent the solution of the given inequalities on the real number line

(2x + 5)/3 > 3x - 3

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

List the elements of the solution set of the inequation

-3 < x – 2 ≤ 9 – 2x; x ∈ N.

Find the range of values of x which satisfies

-2 2/3 <= x + 1/3 < 3 1/3; x in R

Graph these values of x on the number line.

Find the values of x which satisfy the inequation

-2 <= 1/2 - (2x)/3 < 1 5/6; x ∈ N

Graph the solution on the number line

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.

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

Solve the following inequation and graph the solution set on the number line:
2x – 3 < x + 2 ≤ 3x + 5, x ∈ R.

Solve and graph the solution set of:

2x – 9 < 7 and 3x + 9 ≤ 25, x ∈ R

Solve and graph the solution set of:

2x – 9 ≤ 7 and 3x + 9 > 25, x ∈ I

Solve and graph the solution set of:

x + 5 ≥ 4(x - 1) and 3 - 2x < -7 ; x ∈ R .

Solve and graph the solution set of:

3x – 2 > 19 or 3 – 2x ≥ -7, x ∈ R

Solve and graph the solution set of:

5 > p – 1 > 2 or 7 ≤ 2p – 1 ≤ 17, p ∈ R

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

1) Write down A and B in set builder notation/

2) Represent A ∪ B and A ∩ B' on two different number lines

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

x > 3 and 0 < x < 6

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

x < 0 and -3 ≤ x < 1

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

-1 < x ≤ 6 and -2 ≤ x ≤ 3

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

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

Represent on different number lines:

A ∩ B

Given A = {x: -1 < x ≤ 5, x ∈ R} and B = {x: -4 ≤ x < 3, x ∈ R}
Represent on different number lines:

A' ∩ B

Given A = {x: -1 < x ≤ 5, x ∈ R} and B = {x: -4 ≤ x < 3, x ∈ R}
Represent on different number lines:

A – B

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:

1) P ∩ Q

2) P – Q

3) P ∩ Q’

on the different number of lines.

If P = {x: 7x — 4 > 5x + 2, x ∈ R} and Q = {x: x — 19 ≥ 1 — 3x, x ∈ R}, find the range of set P ∩ Q and represent it on a number line.

Find the range of values of x which satisfy:

- 1/3 <= x/2 + 1 2/3 < 5 1/6

The graph in each of the following cases the values of x on the different real number lines:

1) x ∈ W

2) x ∈ Z

3) x ∈ R

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.

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

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

3 >= (x - 4)/2 + x/3 >= 2

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 the number line.

Find the set of values of x satisfying

7x + 3 >= 3x - 5 and x/4 - 5 <= 5/4 - x where x ∈ N

Solve

x/2 + 5 <= x/3 +6 where x is a positive odd integer.

Solve

(2x + 3)/3 >= (3x - 1)/4 where x is a positive even integer.

Solve the inequation

-2 1/2 + 2x <= (4x)/5 <= 4/3 + 2x , x ∈ W.

Graph the solution set on the number line.

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 almost 20.

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

Solve the inequation:
3z – 5 ≤ z + 3 < 5z – 9, z ∈ R.
Graph the solution set on the number line

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

-3 < -1/2 - (2x)/3 ≤ 5/6, x in R

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

4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R

4A4B

## Selina solutions for Class 10 Mathematics chapter 4 - Linear Inequations (In one variable)

Selina solutions for Class 10 Maths chapter 4 (Linear Inequations (In one variable)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 (2018-2019) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 4 Linear Inequations (In one variable) are Representation of Solution on the Number Line, Solving Algebraically and Writing the Solution in Set Notation Form, Linear Inequations in One Unknown.

Using Selina Class 10 solutions Linear Inequations (In one variable) exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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