Can someone please give me some practice questions of inequations of class 8 ?
Answers
Answer:
Question 1.
If the replacement set is the set of natural numbers, solve.
(i) x – 5 < 0
Solution:-
x – 5 < 0
Adding 5, x – 5 + 5 < 0 + 5…
x < 5
Required answer = {1, 2, 3, 4}
(ii) x + 1 < 7
Solution:-
Subtracting 1x + 1 ≤ 7 ⇒ x + 1 – 1 ≤ 7 – 1
x ≤ 6
Required answer = {1, 2, 3, 4, 5, 6}
(iii) 3x – 4 > 6
Solution:-
3x – 4 > 6
Adding 4, 3x – 4 + 4 > 6 + 4
3x > 10
ICSE Class 8 Maths Selina Solutions Chapter 15 Image 1
Required answer = {4, 5, 6,…}
(iv) 4x + 1 > 17
Solution:-
4x + 1 ≥ 17
Subtracting, 4x + 1 – 1 ≥ 17 – 1
4x ≥ 16
Dividing by 4, 4x/4 ≥ (16/4)x ≥ 4
Required answer = {4, 5, 6,…}
Question 2.
If the replacement set = {-6, -3, 0, 3, 6, 9}; find the truth set of the following:
(i) 2x – 1 > 9
Solution:-
2x – 1 > 9
Adding 1, 2x – 1 + 1 > 9 + 1
2x >10
Dividing by 2, x > 5
Required answer = {6, 9}
(ii) 3x + 7 < 1
Solution:-
3x + 7 ≤ 1
Subtracting 7, 3x + 7 – 7 ≤ 1 – 7
3x ≤ -6
x ≤ -2
Required Answer = {-6, -3}
Question 3.
Solve 7 > 3x -8; x ∈ N
Solution:-
7 > 3x – 8
Subtracting 3x, 7 – 3x > 3x – 3x – 8
Subtracting 7, 7 – 7 – 3x > 3x – 3x – 8 – 7
-3x > -15
Dividing by -3, x < 5
Required Answer = {1, 2, 3, 4}
Note: Division by negative number reverses the inequality
Question 4
-17 < 9y – 8; y ∈ Z
Solution:-
-17 < 9y – 8
Adding 8, – 17 + 8 < 9y – 8 + 8
– 9 < 9y
Dividing by 9
-1 < y
Required Answer = {0, 1, 2, 3, 4 …. }
Question 5.
Solve 9x – 7 ≤ 28 + 4x; x ∈ W
Solution:-
9x – 1 ≤ 28 + 4x
Subtracting 4x, 9x – 4x – 7 ≤ 28 + 4x – 4x
5x – 7 ≤ 28
Adding 7, 5x – 7 + 7 ≤ 28 + 7
5x ≤ 35
Dividing by 5, x≤7
Required answer = {0, 1, 2, 3, 4, 5, 6, 7}
Question 6.
Solve 2/3x + 8 < 12; x ∈ W
Solution:-
ICSE Class 8 Maths Selina Solutions Chapter 15 Image 2
Multiplying by 3/2, (2/3) x × (3/2) < 4 × (3/2)
∴ Required answer = {0, 1, 2, 3, 4, 5}
Question 7.
Solve − 5(x + 4) > 30; x ∈ Z
Solution:-
-5(x + 4) > 30
Dividing by -5, ((−5(x+4))/−5) < (30/−5)
Note: Division by a negative number reverses the equality
x + 4 < -6
x + 4 – 4 < – 6 – 4
x < – 10
∴ Required Answer = {-11, -12, -13, …}
Question 8.
Solve the inequation 8 – 2x > x – 5; x ∈ N
Solution:-
8 – 2x ≥ x – 5; x ∈ N
8 + 5 ≥ 2x + x
13 ≥ 3x ⇒ 3x ≤ 13
ICSE Class 8 Maths Selina Solutions Chapter 15 Image 3
x = 1, 2, 3, 4 (x ∈ N)
Solution set = {1, 2, 3, 4}
Question 9.
Solve the inequality 18 -3 (2x – 5) > 12; x ∈ W.
Solution:-
18 – 3(2x – 5) > 12; x ∈ W
18 – 6x + 15 > 12
33 – 12 > 6x
21 > 6x
6x < 21 ⇒ x < 21/6 + 7/2 =3½
But x ∈ W, x = 0, 1, 2, 3
∴ Solution set = {0, 1, 2, 3}
Question 10.
Solve: ((2x+1)/3) + 15 < 17; x ∈ W
Solution:-
((2x+1)/3) + 15 ≤ 17; x ∈ W ((2x+1)/3) ≤ 17 – 15 = 2
2x + 1 ≤ 6 ⇒ 2x ≤ 5
x ≤ 5/2 = 2½
∴ x = 0, 1, 2
∴ Solution set is = {0, 1, 2}
Question 11.
Solve:- 3 + x < 2, x ∈ N
Solution:
-3 + x < 2, x ∈ N
x < 2 – (-3)
x < 2 + 3
x < 5
∴ x = 1, 2, 3, 4 (∵x ∈ N)
∴ Solution set = {1, 2, 3, 4}
Question 12.
Solve: 4x – 5 > 10 – x, x ∈ {0, 1, 2, 3, 4, 5, 6, 7}
Solution:
4x – 5 > 10 – x, x ∈ N
4x + x > 10 + 5
5x > 15
X > 15/5 = 3
∴x=4, 5, 6, 7
Solution set = {4, 5, 6, 7}
Question 13.
Solve: 15 – 2(2x – 1) < 15, x ∈ Z
Solution:
15 – 4x + 2 < 15
17 – 4x < 15
-4x < 15 – 17
-4x < -2
Dividing by -4, (−4/−4)x > −2/−4 = ½
∴x = 1, 2, 3, 4, 5,
∴ Solution set = {1, 2, 3, 4, 5,…}
Question 14.
Solve: (2x + 3)/5 > (4x−1)/2, x ∈ W
Solution:-
(2x + 3)/5 > (4x − 1)/2, x ∈ W
2(2x + 3) > 5(4x – 1)
4x + 6 > 20x – 5
4x – 20x > – 5 – 6
-16x > -11
Dividing by -16, x< (−11/−16) x < (11/16)
∴ x = 0
∴ Solution set = {0}
Solve and graph the solution set on a number line:
Question 15.
x – 5 < – 2; x ∈ N
Solution:-
x – 5 < – 2
Adding 5 to both sides, x – 5 + 5 < – 2 + 5
x < 3