Selina Textbook Solutions: Linear Inequations | Mathematics Class 10 ICSE PDF Download

 Page 1


Linear Inequations (in one variable) 
 
 
Exercise 4A 
Question 1. 
 
 
 
Solution: 
 
 
Question 2. 
State, whether the following statements are true or false: 
(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c 
(iii) If a < b, then ac > bc 
(iv) If a > b, then  
(v) If a – c > b – d, then a + d > b + c 
(vi) If a < b, and c > 0, then a – c > b – c 
Where a, b, c and d are real numbers and c ? 0. 
 
Page 2


Linear Inequations (in one variable) 
 
 
Exercise 4A 
Question 1. 
 
 
 
Solution: 
 
 
Question 2. 
State, whether the following statements are true or false: 
(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c 
(iii) If a < b, then ac > bc 
(iv) If a > b, then  
(v) If a – c > b – d, then a + d > b + c 
(vi) If a < b, and c > 0, then a – c > b – c 
Where a, b, c and d are real numbers and c ? 0. 
 
Solution: 
(i) a < b ? a – c < b – c The given statement is true. 
(ii) If a > b ? a + c > b + c 
The given statement is true. 
(iii) If a < b ? ac < bc The given statement is false. 
(iv) If a > b ?  
The given statement is false. 
(v) If a – c > b – d ? a + d > b + c 
The given statement is true. 
(vi) If a < b ? a – c < b – c (Since, c > 0) 
The given statement is false. 
Question 3. 
If x ? N, find the solution set of inequations. 
(i) 5x + 3 = 2x + 18 
(ii) 3x – 2 < 19 – 4x 
 
Solution: 
(i) 5x + 3 = 2x + 18 
5x – 2x = 18 – 3 
3x = 15 
x = 5 
 
Since, x ? N, therefore solution set is {1, 2, 3, 4, 5}. 
(ii) 3x – 2 < 19 – 4x 
3x + 4x < 19 + 2 
7x < 21 
x < 3 
Since, x ? N, therefore solution set is {1, 2}. 
Question 4. 
 
 
 
Page 3


Linear Inequations (in one variable) 
 
 
Exercise 4A 
Question 1. 
 
 
 
Solution: 
 
 
Question 2. 
State, whether the following statements are true or false: 
(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c 
(iii) If a < b, then ac > bc 
(iv) If a > b, then  
(v) If a – c > b – d, then a + d > b + c 
(vi) If a < b, and c > 0, then a – c > b – c 
Where a, b, c and d are real numbers and c ? 0. 
 
Solution: 
(i) a < b ? a – c < b – c The given statement is true. 
(ii) If a > b ? a + c > b + c 
The given statement is true. 
(iii) If a < b ? ac < bc The given statement is false. 
(iv) If a > b ?  
The given statement is false. 
(v) If a – c > b – d ? a + d > b + c 
The given statement is true. 
(vi) If a < b ? a – c < b – c (Since, c > 0) 
The given statement is false. 
Question 3. 
If x ? N, find the solution set of inequations. 
(i) 5x + 3 = 2x + 18 
(ii) 3x – 2 < 19 – 4x 
 
Solution: 
(i) 5x + 3 = 2x + 18 
5x – 2x = 18 – 3 
3x = 15 
x = 5 
 
Since, x ? N, therefore solution set is {1, 2, 3, 4, 5}. 
(ii) 3x – 2 < 19 – 4x 
3x + 4x < 19 + 2 
7x < 21 
x < 3 
Since, x ? N, therefore solution set is {1, 2}. 
Question 4. 
 
 
 
Solution: 
 
(i) x + 7 = 11 
x = 11 – 7 
x = 4 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2, 3, 4} 
 
(ii) 3x – 1 > 8 
3x > 8 + 1 
x > 3 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {4, 5, 6, …} 
 
(iii) 8 – x > 5 
– x > 5 – 8 
– x > -3 
x < 3 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Page 4


Linear Inequations (in one variable) 
 
 
Exercise 4A 
Question 1. 
 
 
 
Solution: 
 
 
Question 2. 
State, whether the following statements are true or false: 
(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c 
(iii) If a < b, then ac > bc 
(iv) If a > b, then  
(v) If a – c > b – d, then a + d > b + c 
(vi) If a < b, and c > 0, then a – c > b – c 
Where a, b, c and d are real numbers and c ? 0. 
 
Solution: 
(i) a < b ? a – c < b – c The given statement is true. 
(ii) If a > b ? a + c > b + c 
The given statement is true. 
(iii) If a < b ? ac < bc The given statement is false. 
(iv) If a > b ?  
The given statement is false. 
(v) If a – c > b – d ? a + d > b + c 
The given statement is true. 
(vi) If a < b ? a – c < b – c (Since, c > 0) 
The given statement is false. 
Question 3. 
If x ? N, find the solution set of inequations. 
(i) 5x + 3 = 2x + 18 
(ii) 3x – 2 < 19 – 4x 
 
Solution: 
(i) 5x + 3 = 2x + 18 
5x – 2x = 18 – 3 
3x = 15 
x = 5 
 
Since, x ? N, therefore solution set is {1, 2, 3, 4, 5}. 
(ii) 3x – 2 < 19 – 4x 
3x + 4x < 19 + 2 
7x < 21 
x < 3 
Since, x ? N, therefore solution set is {1, 2}. 
Question 4. 
 
 
 
Solution: 
 
(i) x + 7 = 11 
x = 11 – 7 
x = 4 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2, 3, 4} 
 
(ii) 3x – 1 > 8 
3x > 8 + 1 
x > 3 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {4, 5, 6, …} 
 
(iii) 8 – x > 5 
– x > 5 – 8 
– x > -3 
x < 3 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1} 
 
(vi) 18 = 3x – 2 
18 + 2 = 3x 
20 = 3x 
x =  
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {7, 8, 9, …} 
Question 5. 
Solve the inequation: 
3 – 2x = x – 12 given that x ? N. 
 
Solution: 
3 – 2x = x – 12 
-2x – x = -12 – 3 
-3x = -15 
x = 5 
Since, x ? N, therefore, 
Solution set = {1, 2, 3, 4, 5} 
Question 6. 
If 25 – 4x = 16, find: 
(i) the smallest value of x, when x is a real number, 
(ii) the smallest value of x, when x is an integer. 
 
Solution: 
25 – 4x = 16 
-4x = 16 – 25 
-4x = -9 
 
x =  
x = 2.25 
 
(i) The smallest value of x, when x is a real number, is 2.25. 
(ii) The smallest value of x, when x is an integer, is 3. 
Page 5


Linear Inequations (in one variable) 
 
 
Exercise 4A 
Question 1. 
 
 
 
Solution: 
 
 
Question 2. 
State, whether the following statements are true or false: 
(i) a < b, then a – c < b – c (ii) If a > b, then a + c > b + c 
(iii) If a < b, then ac > bc 
(iv) If a > b, then  
(v) If a – c > b – d, then a + d > b + c 
(vi) If a < b, and c > 0, then a – c > b – c 
Where a, b, c and d are real numbers and c ? 0. 
 
Solution: 
(i) a < b ? a – c < b – c The given statement is true. 
(ii) If a > b ? a + c > b + c 
The given statement is true. 
(iii) If a < b ? ac < bc The given statement is false. 
(iv) If a > b ?  
The given statement is false. 
(v) If a – c > b – d ? a + d > b + c 
The given statement is true. 
(vi) If a < b ? a – c < b – c (Since, c > 0) 
The given statement is false. 
Question 3. 
If x ? N, find the solution set of inequations. 
(i) 5x + 3 = 2x + 18 
(ii) 3x – 2 < 19 – 4x 
 
Solution: 
(i) 5x + 3 = 2x + 18 
5x – 2x = 18 – 3 
3x = 15 
x = 5 
 
Since, x ? N, therefore solution set is {1, 2, 3, 4, 5}. 
(ii) 3x – 2 < 19 – 4x 
3x + 4x < 19 + 2 
7x < 21 
x < 3 
Since, x ? N, therefore solution set is {1, 2}. 
Question 4. 
 
 
 
Solution: 
 
(i) x + 7 = 11 
x = 11 – 7 
x = 4 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2, 3, 4} 
 
(ii) 3x – 1 > 8 
3x > 8 + 1 
x > 3 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {4, 5, 6, …} 
 
(iii) 8 – x > 5 
– x > 5 – 8 
– x > -3 
x < 3 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1, 2} 
 
 
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {0, 1} 
 
(vi) 18 = 3x – 2 
18 + 2 = 3x 
20 = 3x 
x =  
 
Since, the replacement set = W (set of whole numbers) 
? Solution set = {7, 8, 9, …} 
Question 5. 
Solve the inequation: 
3 – 2x = x – 12 given that x ? N. 
 
Solution: 
3 – 2x = x – 12 
-2x – x = -12 – 3 
-3x = -15 
x = 5 
Since, x ? N, therefore, 
Solution set = {1, 2, 3, 4, 5} 
Question 6. 
If 25 – 4x = 16, find: 
(i) the smallest value of x, when x is a real number, 
(ii) the smallest value of x, when x is an integer. 
 
Solution: 
25 – 4x = 16 
-4x = 16 – 25 
-4x = -9 
 
x =  
x = 2.25 
 
(i) The smallest value of x, when x is a real number, is 2.25. 
(ii) The smallest value of x, when x is an integer, is 3. 
Question 7. 
 
 
Solution: