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:
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