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Selina solutions for Concise Mathematics Class 10 ICSE chapter 4 - Linear Inequations (In one variable) [Latest edition]

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Concise Mathematics Class 10 ICSE - Shaalaa.com

Chapter 4: Linear Inequations (In one variable)

Exercise 4(A)Exercise 4(B)

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 4 Linear Inequations (In one variable) Exercise Exercise 4(A) [Page 44]

Exercise 4(A) | Q 1.1 | Page 44

State true or false

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

  • True

  • False

Exercise 4(A) | Q 1.2 | Page 44

State true or false

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

  • True

  • False

Exercise 4(A) | Q 1.3 | Page 44

State true or false

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

  • True

  • False

Exercise 4(A) | Q 1.4 | Page 44

State true or false

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

  • True

  • False

Exercise 4(A) | Q 2.1 | Page 44

State, whether the following statements are true or false:

a < b, then a – c < b – c

  • True

  • False

Exercise 4(A) | Q 2.2 | Page 44

State, whether the following statements are true or false:

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

  • True

  • False

Exercise 4(A) | Q 2.3 | Page 44

State, whether the following statements are true or false:

IF a < b, then ac < bc

  • True

  • False

Exercise 4(A) | Q 2.4 | Page 44

State, whether the following statements are true or false:

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

  • True

  • False

Exercise 4(A) | Q 2.5 | Page 44

State, whether the following statements are true or false:

If a – c > b – d, then a + d > b + c

  • True

  • False

Exercise 4(A) | Q 2.6 | Page 44

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

Exercise 4(A) | Q 3.1 | Page 44

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

5x + 3 ≤ 2x + 18

Exercise 4(A) | Q 3.2 | Page 44

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

3x – 2 < 19 – 4x

Exercise 4(A) | Q 4.1 | Page 44

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

`x + 7 <= 11`

Exercise 4(A) | Q 4.2 | Page 44

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

3x - 1 > 8

Exercise 4(A) | Q 4.3 | Page 44

If the replacement set is the set of whole numbers solve

8 - x > 5

Exercise 4(A) | Q 4.4 | Page 44

If the replacement set is the set of whole numbers solve

`7 - 3x >= - 1/2`

Exercise 4(A) | Q 4.5 | Page 44

If the replacement set is the set of whole numbers solve

`x  - 3/2 < 3/2 - x`

Exercise 4(A) | Q 4.6 | Page 44

If the replacement set is the set of whole numbers solve

`18<= 3"x" - 2`

Exercise 4(A) | Q 5 | Page 44

Solve the inequation:

3 – 2x ≥ x – 12 given that x ∈ N.

Exercise 4(A) | Q 6 | Page 44

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.

Exercise 4(A) | Q 7.1 | Page 44

If the replacement set is the set of real numbers solve

`-4x >= - 16`

Exercise 4(A) | Q 7.2 | Page 44

If the replacement set is the set of real numbers solve

`8 - 3x  <= 20`

Exercise 4(A) | Q 7.3 | Page 44

If the replacement set is the set of real numbers solve

`5 + x/4 > x/5 + 9`

Exercise 4(A) | Q 7.4 | Page 44

If the replacement set is the set of real numbers solve

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

Exercise 4(A) | Q 8 | Page 44

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

Exercise 4(A) | Q 9 | Page 44

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

Exercise 4(A) | Q 10 | Page 44

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

Exercise 4(A) | Q 11 | Page 44

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

-5 ≤ 2x – 3 < x + 2

Exercise 4(A) | Q 12 | Page 44

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

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 4 Linear Inequations (In one variable) Exercise Exercise 4(B) [Pages 49 - 50]

Exercise 4(B) | Q 1.1 | Page 49

Represent the following inequalities on real number lines

2x - 1 < 5

Exercise 4(B) | Q 1.2 | Page 49

Represent the following inequalities on real number lines

3x + 1 >= -5

Exercise 4(B) | Q 1.3 | Page 49

Represent the following inequalities on real number lines

`2(2x- 3) <= 6`

Exercise 4(B) | Q 1.4 | Page 49

Represent the following inequalities on real number lines

-4 < x < 4

Exercise 4(B) | Q 1.5 | Page 49

Represent the following inequalities on real number lines

`-2 <= x  < 5`

Exercise 4(B) | Q 1.6 | Page 49

Represent the following inequalities on real number lines

`8 >= x > -3`

Exercise 4(B) | Q 1.7 | Page 49

Represent the following in-equalities on real number line :

−5 < × ≤ −1

Exercise 4(B) | Q 2.1 | Page 49

For graph given write an inequation taking x as the variable

Exercise 4(B) | Q 2.2 | Page 49

For graph given write an inequation taking x as the variable

Exercise 4(B) | Q 2.3 | Page 49

For graph given write an inequation taking x as the variable

Exercise 4(B) | Q 2.4 | Page 49

For graph given write an inequation taking x as the variable

 

Exercise 4(B) | Q 3.1 | Page 49

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

-4 < 3x - 1 < 8

Exercise 4(B) | Q 3.2 | Page 49

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

`x - 1 < 3 -  x <= 5`

Exercise 4(B) | Q 4.1 | Page 49

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

4x - 1 > x + 11

Exercise 4(B) | Q 4.2 | Page 49

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

`7 - x <= 2 - 6x`

Exercise 4(B) | Q 4.3 | Page 49

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

`x + 3 <= 2x + 9`

Exercise 4(B) | Q 4.4 | Page 49

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

2 - 3x > 7 - 5x

Exercise 4(B) | Q 4.5 | Page 49

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

`1 + x >= 5x - 11`

Exercise 4(B) | Q 4.6 | Page 49

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

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

Exercise 4(B) | Q 5 | Page 49

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

Exercise 4(B) | Q 6 | Page 49

List the elements of the solution set of the inequation

-3 < x – 2 ≤ 9 – 2x; x ∈ N.

Exercise 4(B) | Q 7 | Page 49

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.

Exercise 4(B) | Q 8 | Page 49

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

Exercise 4(B) | Q 9 | Page 49

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.

Exercise 4(B) | Q 10 | Page 49

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

Exercise 4(B) | Q 11 | Page 49

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

Exercise 4(B) | Q 12.1 | Page 49

Solve and graph the solution set of:

2x – 9 < 7 and 3x + 9 ≤ 25, x ∈ R

Exercise 4(B) | Q 12.2 | Page 49

Solve and graph the solution set of:

2x – 9 ≤ 7 and 3x + 9 > 25, x ∈ I

Exercise 4(B) | Q 12.3 | Page 49

Solve and graph the solution set of:

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

Exercise 4(B) | Q 13.1 | Page 49

Solve and graph the solution set of:

3x – 2 > 19 or 3 – 2x ≥ -7, x ∈ R

Exercise 4(B) | Q 13.2 | Page 49

Solve and graph the solution set of:

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

Exercise 4(B) | Q 14 | Page 49

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

Exercise 4(B) | Q 15.1 | Page 49

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

x > 3 and 0 < x < 6

Exercise 4(B) | Q 15.2 | Page 49

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

x < 0 and -3 ≤ x < 1

Exercise 4(B) | Q 15.3 | Page 49

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

-1 < x ≤ 6 and -2 ≤ x ≤ 3

Exercise 4(B) | Q 16 | Page 49

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

Exercise 4(B) | Q 17.1 | Page 50

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

Represent on different number lines:

A ∩ B

Exercise 4(B) | Q 17.2 | Page 50

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

A' ∩ B

Exercise 4(B) | Q 17.3 | Page 50

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

A – B

Exercise 4(B) | Q 18 | Page 50

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.

Exercise 4(B) | Q 19 | Page 50

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.

Exercise 4(B) | Q 20 | Page 50

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

Exercise 4(B) | Q 21 | Page 50

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.

Exercise 4(B) | Q 22 | Page 50

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

Exercise 4(B) | Q 23 | Page 50

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

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

Exercise 4(B) | Q 24 | Page 50

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.

Exercise 4(B) | Q 25 | Page 50

Find the set of values of x satisfying

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

 

Exercise 4(B) | Q 26.1 | Page 50

Solve

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

Exercise 4(B) | Q 26.2 | Page 50

Solve

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

Exercise 4(B) | Q 27 | Page 50

Solve the inequation

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

Graph the solution set on the number line.

Exercise 4(B) | Q 28 | Page 50

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.

Exercise 4(B) | Q 29 | Page 50

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

Exercise 4(B) | Q 30 | Page 50

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

Exercise 4(B) | Q 31 | Page 50

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

`-3 < -1/2 - (2x)/3 ≤ 5/6, x in R`

Exercise 4(B) | Q 32 | Page 50

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

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

Exercise 4(B) | Q 33 | Page 50

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

`-"x"/3≤ "x"/2 -1 1/3<1/6, "x" in "R"`

Exercise 4(B) | Q 34 | Page 50

Find the values of x, which satify the inequation

-2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`

Graph the solution set on the number line.

Exercise 4(B) | Q 35 | Page 50

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.

Exercise 4(B) | Q 36 | Page 50

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

-3 (x - 7) ≥ 15 - 7x > `("x" + 1)/3,"x" in "R"`

Exercise 4(B) | Q 37 | Page 50

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

`-8 1/2 < -1/2 - 4x ≤ 71/2, "x" in "I"`

Chapter 4: Linear Inequations (In one variable)

Exercise 4(A)Exercise 4(B)
Concise Mathematics Class 10 ICSE - Shaalaa.com

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

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

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