#### 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 (2018-2019)

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

#### 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

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

#### Selina Selina ICSE Concise Mathematics Class 10 (2018-2019)

#### Textbook solutions for Class 10

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

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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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