Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations (In one variable) Ex 4B

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B.

Other Exercises

Question 1.
Represent the following inequalities on real number lines:
(i) 2x – 1 < 5
(ii) 3x + 1 ≥ – 5
(iii) 2 (2x – 3) ≤ 6
(iv) -4 < x < 4
(v) -2 ≤ x < 5 (vi) 8 ≥ x > -3
(vii) -5 < x ≤ -1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 1.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 1.2

Question 2.
For each graph given below, write an inequation taking x as the variable :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 2.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 2.2

Question 3.
For the following inequations, graph the solution set on the real number line :
(i) – 4 ≤ 3x – 1 < 8
(ii) x – 1 < 3 – x ≤ 5
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 3.

Question 4.
Represent the solution of each of the following inequalities on the real number line :
(i) 4x – 1 > x + 11
(ii) 7 – x ≤ 2 – 6x
(iii) x + 3 ≤ 2x + 9
(iv) 2 – 3x > 1 – 5x
(v) 1 + x ≥ 5x – 11
(vi) \(\frac { 2x + 5 }{ 2 }\) > 3x – 3
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 4.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 4.2

Question 5.
x ∈ {real numbers} and -1 < 3 – 2x ≤ 7, evaluate x and represent it on a number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 5.1

Question 6.
List the elements of the solution set of the inequation – 3 < x – 2 ≤ 9 -2x ; x ∈ N.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 6.1

Question 7.
Find the range of values of x which satisfies
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 7.1
Graph these values of x on the number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 7.2

Question 8.
Find the values of x, which satisfy the inequation:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 8.1
Graph the solution on the number line. (2007)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 8.2

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 real number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 9.1

Question 10.
If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.
Solution:
Here in, 5x – 3 ≤ 5 + 3x ≤ 4x + 2
⇒ 5x – 3 ≤ 5 + 3x and 5 + 3x ≤ 4x + 2
⇒ 5x – 3x ≤ 5 + 3 and 3x – 4x ≤ 2 – 5
⇒ 2x ≤ 8 and – x ≤ – 3
⇒ x ≤ 4 and x ≥ 3
Solution is 3 ≤ x ≤ 4
a = 3 and b = 4

Question 11.
Solve the following inequation and graph the solution set on the number line :
2x – 3 < x + 2 ≤ 3x + 5; x ∈ R.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 11.1

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.
Solution:
(i) 2x – 9 < 7 and 3x + 9 ≤ 25; x ∈ R.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 12.1

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.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 13.1

Question 14.
The diagram represents two inequations A and B on real number lines :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 14.1
(i) Write down A and B in set builder notation.
(ii) Represent A ∩ B and A ∩ B’ on two different number lines.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 14.2

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
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 15.1

Question 16.
Illustrate the set {x : -3 ≤ x < 0 or x > 2 ; x ∈ R} on a real number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 16.1

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
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 17.1

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) P ∩ Q’ on different number lines.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 18.1

Question 19.
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.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 19.1

Question 20.
Find the range of values of x, which satisfy:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 20.1
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.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 20.2

Question 21.
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 an B is on two different number lines. Write down the elements of A ∩ B.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 21.1

Question 22.
Solve the following inequation and represent the solution set on the number line 2x – 5 ≤ 5x + 4< 11, where x ∈ I.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 22.1

Question 23.
Given that x ∈ I, solve the inequation and graph the solution on the number line:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 23.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 23.2

Question 24.
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 a number line. (2005)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 24.1

Question 25.
Find the set of values of x, satisfying:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 25.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 25.2

Question 26.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 26.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 26.2

Question 27.
Solve the inequation:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 27.1
Graph the solution set on the number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 27.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 27.3

Question 28.
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 atmost 20.
Solution:
Let first positive integer = x
Then, second integer = x + 1
and third integer = x + 2
According to the condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 28.1

Question 29.
Solve the given inequation and graph the solution on the number line.
2y – 3 < y + 1 < 4y + 7; y ∈ R (2008)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 29.1

Question 30.
Solve the inequation:
3z – 5 ≤ z + 3 < 5z – 9; z ∈ R.
Graph the solution set on the number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 30.1

Question 31.
Solve the following inequation and represent the solution set on the number line.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 31.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 31.2

Question 32.
Solve the following inequation and represent the solution set on the number line:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 32.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 32.2

Question 33.
Solve the following inequation, write the solution set and represent it on the number
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 33.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 33.2

Question 34.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 34.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 34.2

Question 35.
Solve the following inequation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Represent the solution on a real number line. (2015)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 35.1

Question 36.
Solve the following inequation, write the solution set and represent it on the number line.
-3 (x – 7) ≥ 15 – 7x > \(\frac { x + 1 }{ 3 }\), x ∈ R. (2016)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 36.1

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