#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

#### Selina Selina ICSE Concise Mathematics Class 10

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

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

State true or false

`x < -y => -x > y`

State true or false

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

State true or false

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

State true or false

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

State, whether the following statements are true or false:

a < b, then a – c < b – c

State, whether the following statements are true or false:

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

State, whether the following statements are true or false:

IF a < b, then ac < bc

State, whether the following statements are true or false:

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

State, whether the following statements are true or false:

If a – c > b – d, then a + d > b + c

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.

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) 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

#### Selina Selina ICSE Concise Mathematics Class 10

#### Textbook solutions for Class 10

## 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 solutions in a manner that help students grasp basic concepts better and faster.

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

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