EduSahara™ Assignment
Name : Linear Inequations
Chapter : Linear Inequations
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
Solve the inequation
(
9
x
−
81
)
<
0
,
x
∈
Z
(i)
{9,8,7,6,5,...}
(ii)
{9,10,11,12,13,...}
(iii)
{8,7,6,5,4,...}
(iv)
{10,11,12,13,14,...}
Question
2
2.
Solve the inequation
(
x
+
2
)
>
0
,
x
∈
Z
(i)
{-1,0,1,2,3,...}
(ii)
{-3,-4,-5,-6,-7,...}
(iii)
{-2,-1,0,1,2,...}
(iv)
{-2,-3,-4,-5,-6,...}
Question
3
3.
Solve the inequation
(
9
x
−
54
)
≤
0
,
x
∈
Z
(i)
{7,8,9,10,11,...}
(ii)
{5,4,3,2,1,...}
(iii)
{6,5,4,3,2,...}
(iv)
{6,7,8,9,10,...}
Question
4
4.
Solve the inequation
(
−
7
x
−
7
)
≥
0
,
x
∈
Z
(i)
{-2,-3,-4,-5,-6,...}
(ii)
{-1,-2,-3,-4,-5,...}
(iii)
{-1,0,1,2,3,...}
(iv)
{0,1,2,3,4,...}
Question
5
5.
Find the solution set for the given inequation
(
6
x
+
36
)
<
0
,
where the replacement set is
{-4,-5,-6,-7,-8,-9,-10}
(i)
{-7,-8,-9,-10,-11}
(ii)
{-6,-5,-4,-3,-2}
(iii)
{-7,-8,-9,-10}
(iv)
{-6,-7,-8,-9,-10}
(v)
{-5,-4,-3,-2,-1}
Question
6
6.
Find the solution set for the given inequation
(
9
x
+
54
)
>
0
,
where the replacement set is
{-8,-7,-6,-5,-4,-3,-2}
(i)
{-7,-8,-9,-10,-11}
(ii)
{-6,-7,-8,-9,-10}
(iii)
{-6,-5,-4,-3,-2}
(iv)
{-5,-4,-3,-2}
(v)
{-5,-4,-3,-2,-1}
Question
7
7.
Find the solution set for the given inequation
(
−
7
x
+
7
)
≤
0
,
where the replacement set is
{-2,-1,0,1,2,3,4}
(i)
{1,0,-1,-2,-3}
(ii)
{1,2,3,4}
(iii)
{0,-1,-2,-3,-4}
(iv)
{1,2,3,4,5}
(v)
{2,3,4,5,6}
Question
8
8.
Find the solution set for the given inequation
(
3
x
−
12
)
≥
0
,
where the replacement set is
{1,2,3,4,5,6,7}
(i)
{5,6,7,8,9}
(ii)
{4,5,6,7,8}
(iii)
{4,5,6,7}
(iv)
{3,2,1,0,-1}
(v)
{4,3,2,1,0}
Question
9
9.
Which of the following is an inequation?
(i)
(
−
5
x
−
7
)
>
0
,
x
∈
Z
(ii)
2
(iii)
(
7
x
+
5
)
=
0
(iv)
(
5
x
+
6
)
Question
10
10.
Which of the following is not an inequation?
(i)
(
5
x
+
5
)
≥
0
,
x
∈
Z
(ii)
(
−
3
x
−
5
)
<
(
−
3
)
,
x
∈
Z
(iii)
(
−
5
x
+
1
)
=
3
(iv)
(
2
x
+
3
)
>
9
,
x
∈
Z
(v)
(
−
8
x
−
5
)
≤
(
−
6
)
,
x
∈
Z
Question
11
11.
Which of the following is not an inequation?
(i)
(
3
x
+
6
)
>
(
−
8
x
+
9
)
,
x
∈
Z
(ii)
(
−
9
x
−
5
)
≥
(
8
x
−
8
)
,
x
∈
Z
(iii)
(
−
2
x
+
2
)
=
(
−
3
x
−
9
)
(iv)
(
5
x
−
1
)
<
(
−
x
+
6
)
,
x
∈
Z
(v)
(
x
+
2
)
≤
(
−
x
+
2
)
,
x
∈
Z
Question
12
12.
Which of the following inequations is the same as
(
−
2
x
)
<
(
4
x
−
3
)
,
x
∈
Z
(i)
(
−
2
x
)
<
(
−
3
x
−
3
)
,
x
∈
Z
(ii)
(
−
9
x
)
>
(
4
x
−
3
)
,
x
∈
Z
(iii)
(
−
2
x
)
>
(
−
3
x
−
3
)
,
x
∈
Z
(iv)
(
−
9
x
)
<
(
−
3
x
−
3
)
,
x
∈
Z
(v)
(
−
9
x
)
<
(
4
x
−
3
)
,
x
∈
Z
Question
13
13.
Which of the following inequations is the same as
(
4
x
−
3
)
<
(
8
x
+
7
)
,
x
∈
Z
(i)
(
6
x
−
2
)
>
(
8
x
+
7
)
,
x
∈
Z
(ii)
(
6
x
−
2
)
<
(
8
x
+
7
)
,
x
∈
Z
(iii)
(
4
x
−
3
)
>
(
10
x
+
8
)
,
x
∈
Z
(iv)
(
6
x
−
2
)
<
(
10
x
+
8
)
,
x
∈
Z
(v)
(
4
x
−
3
)
<
(
10
x
+
8
)
,
x
∈
Z
Question
14
14.
Which of the following inequations is the same as
(
−
x
+
8
)
≤
(
−
5
x
−
9
)
,
x
∈
Z
(i)
(
−
x
+
8
)
<
(
−
8
x
−
9
)
,
x
∈
Z
(ii)
(
−
4
x
+
8
)
>
(
−
5
x
−
9
)
,
x
∈
Z
(iii)
(
−
4
x
+
8
)
≤
(
−
8
x
−
9
)
,
x
∈
Z
(iv)
(
−
x
+
8
)
>
(
−
8
x
−
9
)
,
x
∈
Z
(v)
(
−
4
x
+
8
)
<
(
−
5
x
−
9
)
,
x
∈
Z
Question
15
15.
Which of the following inequations is the same as
(
6
x
+
4
)
≤
(
8
x
−
5
)
,
x
∈
Z
(i)
(
13
x
+
3
)
<
(
8
x
−
5
)
,
x
∈
Z
(ii)
(
13
x
+
3
)
>
(
8
x
−
5
)
,
x
∈
Z
(iii)
(
6
x
+
4
)
<
(
15
x
−
6
)
,
x
∈
Z
(iv)
(
13
x
+
3
)
≤
(
15
x
−
6
)
,
x
∈
Z
(v)
(
6
x
+
4
)
>
(
15
x
−
6
)
,
x
∈
Z
Question
16
16.
Which of the following inequations is the same as
(
7
x
−
6
)
>
(
−
3
x
+
8
)
,
x
∈
Z
(i)
(
7
x
−
6
)
<
(
−
5
x
+
3
)
,
x
∈
Z
(ii)
(
5
x
−
11
)
>
(
−
5
x
+
3
)
,
x
∈
Z
(iii)
(
5
x
−
11
)
>
(
−
3
x
+
8
)
,
x
∈
Z
(iv)
(
7
x
−
6
)
>
(
−
5
x
+
3
)
,
x
∈
Z
(v)
(
5
x
−
11
)
<
(
−
3
x
+
8
)
,
x
∈
Z
Question
17
17.
Which of the following inequations is the same as
(
6
x
+
5
)
>
(
2
x
+
1
)
,
x
∈
Z
(i)
(
6
x
+
5
)
<
(
−
7
x
−
3
)
,
x
∈
Z
(ii)
(
−
3
x
+
1
)
<
(
2
x
+
1
)
,
x
∈
Z
(iii)
(
−
3
x
+
1
)
>
(
−
7
x
−
3
)
,
x
∈
Z
(iv)
(
6
x
+
5
)
>
(
−
7
x
−
3
)
,
x
∈
Z
(v)
(
−
3
x
+
1
)
>
(
2
x
+
1
)
,
x
∈
Z
Question
18
18.
Which of the following inequations is the same as
(
7
x
+
3
)
≥
(
−
9
x
+
5
)
,
x
∈
Z
(i)
(
7
x
+
3
)
>
(
−
14
x
−
4
)
,
x
∈
Z
(ii)
(
7
x
+
3
)
<
(
−
14
x
−
4
)
,
x
∈
Z
(iii)
(
2
x
−
6
)
<
(
−
9
x
+
5
)
,
x
∈
Z
(iv)
(
2
x
−
6
)
≥
(
−
14
x
−
4
)
,
x
∈
Z
(v)
(
2
x
−
6
)
>
(
−
9
x
+
5
)
,
x
∈
Z
Question
19
19.
Which of the following inequations is not the same as
(
−
x
)
<
(
9
x
+
6
)
,
x
∈
Z
(i)
(
−
5
x
+
1
)
<
(
5
x
+
7
)
,
x
∈
Z
(ii)
(
4
x
−
7
)
<
(
14
x
−
1
)
,
x
∈
Z
(iii)
(
−
3
x
−
9
)
<
(
7
x
−
3
)
,
x
∈
Z
(iv)
(
−
6
x
+
5
)
<
(
4
x
+
11
)
,
x
∈
Z
(v)
(
4
x
−
7
)
<
(
5
x
+
7
)
,
x
∈
Z
Question
20
20.
Which of the following inequations is not the same as
(
6
x
−
1
)
<
(
9
x
−
3
)
,
x
∈
Z
(i)
(
9
x
+
5
)
<
(
12
x
+
3
)
,
x
∈
Z
(ii)
(
13
x
+
7
)
<
(
x
+
6
)
,
x
∈
Z
(iii)
(
8
x
+
4
)
<
(
11
x
+
2
)
,
x
∈
Z
(iv)
(
13
x
+
7
)
<
(
16
x
+
5
)
,
x
∈
Z
(v)
(
−
2
x
+
8
)
<
(
x
+
6
)
,
x
∈
Z
Question
21
21.
Which of the following inequations is not the same as
(
−
2
x
+
8
)
≤
(
−
8
x
+
4
)
,
x
∈
Z
(i)
(
2
x
+
8
)
≤
(
−
4
x
+
4
)
,
x
∈
Z
(ii)
(
−
9
x
+
7
)
≤
(
−
15
x
+
3
)
,
x
∈
Z
(iii)
(
3
x
+
7
)
≤
(
−
3
x
+
3
)
,
x
∈
Z
(iv)
(
−
5
x
+
15
)
≤
(
−
11
x
+
11
)
,
x
∈
Z
(v)
(
−
9
x
+
7
)
≤
(
−
3
x
+
3
)
,
x
∈
Z
Question
22
22.
Which of the following inequations is not the same as
(
−
4
x
−
6
)
≤
8
x
,
x
∈
Z
(i)
(
−
9
x
−
6
)
≤
3
x
,
x
∈
Z
(ii)
(
−
5
x
−
7
)
≤
(
11
x
+
7
)
,
x
∈
Z
(iii)
(
−
5
x
−
7
)
≤
(
7
x
−
1
)
,
x
∈
Z
(iv)
(
−
x
+
1
)
≤
(
11
x
+
7
)
,
x
∈
Z
(v)
(
−
2
)
≤
(
12
x
+
4
)
,
x
∈
Z
Question
23
23.
The solution set of the inequality
(
8
x
+
5
)
<
(
−
7
x
−
6
)
,
x
∈
Z
is
(i)
{-1,-2,-3,-4,-5,...}
(ii)
{18,19,20,21,22,...}
(iii)
{0,1,2,3,4,...}
(iv)
{1,0,-1,-2,-3,...}
Question
24
24.
The solution set of the inequality
(
3
x
−
9
)
>
(
−
4
x
−
2
)
,
x
∈
Z
is
(i)
{2,3,4,5,6,...}
(ii)
{-1,-2,-3,-4,-5,...}
(iii)
{1,2,3,4,5,...}
(iv)
{0,-1,-2,-3,-4,...}
(v)
{-2,-1,0,1,2,...}
Question
25
25.
The solution set of the inequality
(
−
3
x
−
8
)
≤
(
−
9
x
+
3
)
,
x
∈
Z
is
(i)
{2,3,4,5,6,...}
(ii)
{1,0,-1,-2,-3,...}
(iii)
{5,4,3,2,1,...}
(iv)
{0,1,2,3,4,...}
Question
26
26.
The solution set of the inequality
(
−
3
x
+
9
)
≤
(
−
9
)
,
x
∈
Z
is
(i)
{5,4,3,2,1,...}
(ii)
{6,7,8,9,10,...}
(iii)
{6,5,4,3,2,...}
(iv)
{0,-1,-2,-3,-4,...}
(v)
{0,1,2,3,4,...}
Question
27
27.
The solution set of the inequality
(
−
9
x
+
7
)
≥
5
,
x
∈
Z
is
(i)
{-1,-2,-3,-4,-5,...}
(ii)
{1,2,3,4,5,...}
(iii)
{0,-1,-2,-3,-4,...}
Question
28
28.
The simplified form of the inequality
(
−
3
x
+
4
)
<
3
,
x
∈
Z
is
(i)
x
≥
0
,
x
∈
Z
(ii)
x
<
2
3
,
x
∈
Z
(iii)
x
>
2
3
,
x
∈
Z
(iv)
x
≤
0
,
x
∈
Z
(v)
x
>
1
3
,
x
∈
Z
Question
29
29.
The simplified form of the inequality
(
−
6
x
−
9
)
>
5
,
x
∈
Z
is
(i)
x
<
(
−
13
6
)
,
x
∈
Z
(ii)
x
>
(
−
13
6
)
,
x
∈
Z
(iii)
x
≤
(
−
5
2
)
,
x
∈
Z
(iv)
x
≥
(
−
5
2
)
,
x
∈
Z
(v)
x
<
(
−
7
3
)
,
x
∈
Z
Question
30
30.
The simplified form of the inequality
(
−
5
x
−
8
)
≤
(
−
6
)
,
x
∈
Z
is
(i)
x
≥
(
−
2
5
)
,
x
∈
Z
(ii)
x
<
(
−
1
5
)
,
x
∈
Z
(iii)
x
>
(
−
1
5
)
,
x
∈
Z
(iv)
x
≥
(
−
3
5
)
,
x
∈
Z
(v)
x
≤
(
−
3
5
)
,
x
∈
Z
Question
31
31.
The simplified form of the inequality
(
−
2
x
+
7
)
≥
(
−
6
)
,
x
∈
Z
is
(i)
x
≤
13
2
,
x
∈
Z
(ii)
x
>
7
,
x
∈
Z
(iii)
x
<
7
,
x
∈
Z
(iv)
x
≥
6
,
x
∈
Z
(v)
x
≤
6
,
x
∈
Z
Question
32
32.
The simplified form of the inequality
(
3
x
+
1
)
<
(
9
x
−
4
)
,
x
∈
Z
is
(i)
x
<
1
,
x
∈
Z
(ii)
x
≤
2
3
,
x
∈
Z
(iii)
x
>
5
6
,
x
∈
Z
(iv)
x
≥
2
3
,
x
∈
Z
(v)
x
>
1
,
x
∈
Z
Question
33
33.
The simplified form of the inequality
(
−
9
x
−
6
)
>
(
−
x
−
6
)
,
x
∈
Z
is
(i)
x
≤
(
−
1
8
)
,
x
∈
Z
(ii)
x
<
1
8
,
x
∈
Z
(iii)
x
≥
(
−
1
8
)
,
x
∈
Z
(iv)
x
<
0
,
x
∈
Z
(v)
x
>
1
8
,
x
∈
Z
Question
34
34.
The simplified form of the inequality
(
−
3
x
−
9
)
≤
(
−
2
x
−
9
)
,
x
∈
Z
is
(i)
x
≥
(
−
1
)
,
x
∈
Z
(ii)
x
<
1
,
x
∈
Z
(iii)
x
≤
(
−
1
)
,
x
∈
Z
(iv)
x
>
1
,
x
∈
Z
(v)
x
≥
0
,
x
∈
Z
Question
35
35.
The simplified form of the inequality
(
x
−
4
)
≥
(
−
5
x
+
6
)
,
x
∈
Z
is
(i)
x
>
3
2
,
x
∈
Z
(ii)
x
≥
11
6
,
x
∈
Z
(iii)
x
≤
11
6
,
x
∈
Z
(iv)
x
<
3
2
,
x
∈
Z
(v)
x
≥
5
3
,
x
∈
Z
Question
36
36.
Which of the following inequations is the same as
(
−
8
x
+
8
)
≥
(
−
7
x
+
2
)
,
x
∈
Z
(i)
(
−
8
x
+
8
)
>
(
−
9
x
+
5
)
,
x
∈
Z
(ii)
(
−
10
x
+
11
)
>
(
−
7
x
+
2
)
,
x
∈
Z
(iii)
(
−
10
x
+
11
)
<
(
−
7
x
+
2
)
,
x
∈
Z
(iv)
(
−
8
x
+
8
)
<
(
−
9
x
+
5
)
,
x
∈
Z
(v)
(
−
10
x
+
11
)
≥
(
−
9
x
+
5
)
,
x
∈
Z
Question
37
37.
Which of the following statements are true?
a)
Dividing same negative number on both sides does not change the inequality
b)
Multiplying same negative number on both sides does not change the inequality
c)
Subtracting same number on both sides does not change the inequality
d)
Dividing same positive number on both sides does not change the inequality
e)
Multiplying same positive number on both sides does not change the inequality
f)
Adding same number on both sides does not change the inequality
(i)
{c,d,e,f}
(ii)
{b,d}
(iii)
{a,b,e}
(iv)
{a,c}
(v)
{a,f,c}
Question
38
38.
Which of the following inequations is not the same as
(
−
3
x
+
8
)
<
(
−
2
x
−
2
)
,
x
∈
Z
(i)
(
21
x
−
56
)
>
(
14
x
+
14
)
,
x
∈
Z
(ii)
(
24
x
−
64
)
>
(
16
x
+
16
)
,
x
∈
Z
(iii)
(
−
6
x
+
16
)
<
(
14
x
+
14
)
,
x
∈
Z
(iv)
(
9
x
−
24
)
>
(
6
x
+
6
)
,
x
∈
Z
(v)
(
−
6
x
+
16
)
<
(
−
4
x
−
4
)
,
x
∈
Z
Question
39
39.
Find the solution set of given inequality
(
−
2
x
−
10
)
<
0
,
x
∈
Z
(i)
{-5,-4,-3,-2,...}
(ii)
{-4,-3,-2,-1,...}
(iii)
{-5,-6,-7,-8,...}
(iv)
{-6,-7,-8,-9,...}
Question
40
40.
Find the solution set of given inequality
(
−
3
x
−
12
)
>
0
,
x
∈
Z
(i)
{-5,-6,-7,-8,...}
(ii)
{-4,-5,-6,-7,...}
(iii)
{-4,-3,-2,-1,...}
(iv)
{-3,-2,-1,0,...}
Question
41
41.
Find the solution set of given inequality
2
x
≤
0
,
x
∈
Z
(i)
{-1,-2,-3,-4,...}
(ii)
{1,2,3,4,...}
(iii)
{0,-1,-2,-3,...}
(iv)
{0,1,2,3,...}
Question
42
42.
Find the solution set of given inequality
(
−
9
x
−
63
)
≥
0
,
x
∈
Z
(i)
{-7,-8,-9,-10,...}
(ii)
{-6,-5,-4,-3,...}
(iii)
{-8,-9,-10,-11,...}
(iv)
{-7,-6,-5,-4,...}
Question
43
43.
Find the solution set of
2
<
(
−
6
x
+
7
)
<
28
,
x
∈
Z
(i)
{0,-1,-2,-3}
(ii)
{-1,-2,-3,-4}
(iii)
{2,1,0,-1}
(iv)
{-2,-3,-4,-5}
(v)
{1,0,-1,-2}
Question
44
44.
Find the solution set of
(
−
15
)
>
(
−
6
x
−
5
)
>
(
−
29
)
,
x
∈
Z
(i)
{3,4}
(ii)
{2,3}
(iii)
{4,5}
(iv)
{0,1}
(v)
{1,2}
Question
45
45.
Find the solution set of
7
≤
(
−
x
−
9
)
≤
18
,
x
∈
Z
(i)
{-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28}
(ii)
{-16,-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27}
(iii)
{-14,-15,-16,-17,-18,-19,-20,-21,-22,-23,-24,-25}
(iv)
{-15,-16,-17,-18,-19,-20,-21,-22,-23,-24,-25,-26}
(v)
{-18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29}
Question
46
46.
Find the solution set of
(
−
3
)
≥
(
−
3
x
−
9
)
≥
(
−
20
)
,
x
∈
Z
(i)
{-1,0,1,2,3,4}
(ii)
{-4,-3,-2,-1,0,1}
(iii)
{-3,-2,-1,0,1,2}
(iv)
{0,1,2,3,4,5}
(v)
{-2,-1,0,1,2,3}
Question
47
47.
Find the solution set of
14
<
(
5
x
−
3
)
≤
29
,
x
∈
Z
(i)
{5,6,7}
(ii)
{2,3,4}
(iii)
{3,4,5}
(iv)
{6,7,8}
(v)
{4,5,6}
Question
48
48.
Find the solution set of
5
>
(
9
x
+
4
)
≥
(
−
24
)
,
x
∈
Z
(i)
{0,-1,-2,-3}
(ii)
{-2,-3,-4,-5}
(iii)
{1,0,-1,-2}
(iv)
{-1,-2,-3,-4}
(v)
{2,1,0,-1}
Question
49
49.
Find the solution set of
(
−
4
)
≤
(
−
4
x
+
2
)
<
20
,
x
∈
Z
(i)
{2,1,0,-1,-2,-3}
(ii)
{0,-1,-2,-3,-4,-5}
(iii)
{3,2,1,0,-1,-2}
(iv)
{1,0,-1,-2,-3,-4}
(v)
{-1,-2,-3,-4,-5,-6}
Question
50
50.
Find the solution set of
9
≥
(
6
x
−
5
)
>
(
−
17
)
,
x
∈
Z
(i)
{4,3,2,1}
(ii)
{0,-1,-2,-3}
(iii)
{3,2,1,0}
(iv)
{1,0,-1,-2}
(v)
{2,1,0,-1}
Assignment Key
1) (iii)
2) (i)
3) (iii)
4) (ii)
5) (iii)
6) (iv)
7) (ii)
8) (iii)
9) (i)
10) (iii)
11) (iii)
12) (iv)
13) (iv)
14) (iii)
15) (iv)
16) (ii)
17) (iii)
18) (iv)
19) (v)
20) (ii)
21) (v)
22) (ii)
23) (i)
24) (i)
25) (ii)
26) (ii)
27) (iii)
28) (v)
29) (v)
30) (i)
31) (i)
32) (iii)
33) (iv)
34) (v)
35) (v)
36) (v)
37) (i)
38) (iii)
39) (ii)
40) (i)
41) (iii)
42) (i)
43) (i)
44) (ii)
45) (ii)
46) (v)
47) (v)
48) (i)
49) (iv)
50) (v)
