## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 12 Linear Equations and Inequalities in One Variable Ex 12.3

Question 1.

If the replacement set = {-7, -5, -3, – 1, 3}, find the solution set of:

(i) x > – 2

(ii) x < – 2

(iii) x > 2

(iv) -5 < x ≤ 5

(v) -8 < x < 1

(vi) 0 ≤ x ≤ 4

Solution:

Question 2.

Represent the solution of the following inequalities graphically:

(i) x ≤ 4, x ϵ N

(ii) x < 5, x ϵ W

(iii) -3 ≤ x < 3, x ϵ I

Solution:

Question 3.

If the replacement set is {-6, -4, -2, 0, 2, 4, 6}, then represent the solution set of the inequality – 4 ≤ x < 4 grahically.

Solution:

Question 4.

Find the solution set of the inequality x < 4 if the replacement set is

(i) {1, 2, 3, ………..,10}

(ii) {-1, 0, 1, 2, 5, 8}

(iii) {-5, 10}

(iv) {5, 6, 7, 8, 9, 10}

Solution:

Question 5.

If the replacement set = {-6, -3, 0, 3, 6, 9, 12}, find the truth set of the following.:

(i) 2x – 3 > 7

(ii) 3x + 8 ≤ 2

(iii) -3 < 1 – 2x

Solution:

Question 6.

Solve the following inequations:

(i) 4x + 1 < 17, x ϵ N

(ii) 4x + 1 ≤ 17, x ϵ W

(iii) 4 > 3x – 11, x ϵ N

(iv) -17 ≤ 9x – 8, x 6ϵ Z

Solution:

Question 7.

Solve the following inequations :

Solution:

Question 8.

Solve the following inequations:

(i) 2x – 3 < x + 2, x ϵ N

(ii) 3 – x ≤ 5 – 3x, x ϵ W

(iii) 3 (x – 2) < 2 (x -1), x ϵ W

(iv) \(\frac{3}{2}-\frac{x}{2}\) > -1, x ϵ N

Solution:

Question 9.

If the replacement set is {-3, -2, -1,0, 1, 2, 3} , solve the inequation \(\frac{3 x-1}{2}<2\). represent its solution on the number line.

Solution:

Question 10.

Solve \(\frac{x}{3}+\frac{1}{4}<\frac{x}{6}+\frac{1}{2}\), x ϵ W. Also represent its solution on the number line.

Solution:

Question 11.

Solve the following inequations and graph their solutions on a number line

(i) -4 ≤ 4x < 14, x ϵ N

(ii) -1 < \(\frac{x}{2}\) + 1 ≤ 3, x ϵ I

Solution: