EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Inequations
Grade : ICSE Grade VIII
License : Non Commercial Use
Question 1
1.
    • The simplified form of the inequality
    • (
      2
      x
      −
      1
      		)
      ≤
      (
      8
      x
      +
      2
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≥
    (
    −
    1
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    (
    −
    2
    3
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    <
    (
    −
    1
    3
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    (
    −
    2
    3
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    >
    (
    −
    1
    3
    		)
    ,
    x
    ∈
    Z
Question 2
2.
    • Identify the solution for the inequality
    • (
      −
      10
      		)
      >
      (
      −
      8
      x
      −
      4
      		)
      >
      (
      −
      22
      		)
      ,
      x
      ∈
      Z
  • (i)
    II
  • (ii)
    IV
  • (iii)
    I
  • (iv)
    III
Question 3
3.
    • Which of the following inequations is the same as
    • (
      3
      x
      +
      1
      		)
      ≤
      (
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    5
    x
    −
    7
    		)
    <
    (
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    5
    x
    −
    7
    		)
    ≤
    (
    3
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    3
    x
    +
    1
    		)
    <
    (
    3
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    5
    x
    −
    7
    		)
    >
    (
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    3
    x
    +
    1
    		)
    >
    (
    3
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
Question 4
4.
    • Identify the solution for the inequality
    • (
      −
      2
      x
      +
      10
      		)
      ≥
      0
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    III
  • (iii)
    I
  • (iv)
    II
Question 5
5.
    • Which of the following inequations is not the same as
    • (
      −
      9
      x
      +
      2
      		)
      ≤
      (
      6
      x
      −
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    14
    x
    +
    5
    		)
    ≤
    (
    2
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    8
    x
    −
    2
    		)
    ≤
    (
    7
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    13
    x
    +
    1
    		)
    ≤
    (
    2
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    18
    x
    −
    7
    		)
    ≤
    (
    −
    3
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    14
    x
    +
    5
    		)
    ≤
    (
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
Question 6
6.
    • Find the solution set of
    • (
      −
      5
      		)
      ≥
      (
      −
      8
      x
      +
      6
      		)
      ≥
      (
      −
      17
      		)
      ,
      x
      ∈
      Z
  • (i)
    {3}
  • (ii)
    {0}
  • (iii)
    {4}
  • (iv)
    {2}
  • (v)
    {1}
Question 7
7.
    • The simplified form of the inequality
    • (
      −
      7
      x
      +
      4
      		)
      ≤
      9
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≤
    (
    −
    6
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    (
    −
    5
    7
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    <
    (
    −
    4
    7
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    >
    (
    −
    4
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≥
    (
    −
    6
    7
    		)
    ,
    x
    ∈
    Z
Question 8
8.
    • Find the solution set of
    • 11
      ≤
      (
      2
      x
      −
      3
      		)
      ≤
      19
      ,
      x
      ∈
      Z
  • (i)
    {6,7,8,9,10}
  • (ii)
    {5,6,7,8,9}
  • (iii)
    {7,8,9,10,11}
  • (iv)
    {8,9,10,11,12}
  • (v)
    {9,10,11,12,13}
Question 9
9.
    • Identify the solution for the inequality
    • (
      −
      4
      		)
      >
      (
      −
      9
      x
      −
      9
      		)
      ≥
      (
      −
      15
      		)
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    III
  • (iii)
    I
  • (iv)
    II
Question 10
10.
    • Identify the solution for the inequality
    • (
      −
      9
      x
      +
      27
      		)
      <
      0
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    II
  • (iii)
    I
  • (iv)
    III
Question 11
11.
    • Which of the following figures represents the solution set
    • {3,2,1,0,-1,-2,...}
  • (i)
    IV
  • (ii)
    II
  • (iii)
    III
  • (iv)
    I
Question 12
12.
    • Identify the solution for the inequality
    • 2
      ≤
      (
      −
      3
      x
      −
      7
      		)
      ≤
      25
      ,
      x
      ∈
      Z
  • (i)
    II
  • (ii)
    III
  • (iii)
    I
  • (iv)
    IV
Question 13
13.
    • Which of the following figures represents the solution set
    • {4,5,6,7,8,9,...}
  • (i)
    III
  • (ii)
    IV
  • (iii)
    I
  • (iv)
    II
Question 14
14.
    • Which of the following inequations is not the same as
    • (
      8
      x
      +
      6
      		)
      ≤
      (
      −
      5
      x
      −
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    9
    x
    +
    5
    		)
    ≤
    (
    −
    4
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (ii)
    0
    ≤
    (
    −
    7
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    6
    x
    +
    11
    		)
    ≤
    (
    −
    7
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    0
    ≤
    (
    −
    13
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≤
    (
    −
    12
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
Question 15
15.
    • Find the solution set for the given inequation
    • (
      4
      x
      −
      4
      		)
      >
      0
      ,
      where the replacement set is
      {-1,0,1,2,3,4,5}
  • (i)
    {2,3,4,5}
  • (ii)
    {1,2,3,4,5}
  • (iii)
    {1,0,-1,-2,-3}
  • (iv)
    {2,3,4,5,6}
  • (v)
    {0,-1,-2,-3,-4}
Question 16
16.
Which of the following statements are true?
a)
Subtracting same number on both sides does not change the inequality
b)
Adding same number on both sides does not change the inequality
c)
Dividing same negative 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 negative number on both sides does not change the inequality
f)
Multiplying same positive number on both sides does not change the inequality
  • (i)
    {a,b,d,f}
  • (ii)
    {c,f,a}
  • (iii)
    {c,a}
  • (iv)
    {c,e,d}
  • (v)
    {e,b}
Question 17
17.
    • The simplified form of the inequality
    • (
      −
      6
      x
      +
      4
      		)
      >
      (
      −
      x
      +
      8
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    (
    −
    4
    5
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≤
    (
    −
    1
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    >
    (
    −
    3
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    <
    (
    −
    3
    5
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≥
    (
    −
    1
    		)
    ,
    x
    ∈
    Z
Question 18
18.
    • Identify the solution for the inequality
    • (
      −
      2
      		)
      <
      (
      7
      x
      +
      5
      		)
      <
      11
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    I
  • (iii)
    III
  • (iv)
    II
Question 19
19.
    • Identify the solution for the inequality
    • 7
      x
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    II
  • (ii)
    III
  • (iii)
    IV
  • (iv)
    I
Question 20
20.
    • Which of the following inequations is not the same as
    • (
      3
      x
      +
      4
      		)
      >
      (
      −
      5
      x
      +
      6
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    12
    x
    +
    5
    		)
    >
    (
    4
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    9
    x
    −
    2
    		)
    >
    x
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    3
    x
    +
    5
    		)
    >
    (
    −
    11
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    4
    x
    +
    9
    		)
    >
    (
    −
    4
    x
    +
    11
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    3
    x
    +
    5
    		)
    >
    (
    −
    4
    x
    +
    11
    		)
    ,
    x
    ∈
    Z
Question 21
21.
    • Which of the following inequations is the same as
    • (
      −
      6
      x
      −
      3
      		)
      ≤
      (
      4
      x
      −
      4
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    6
    x
    −
    3
    		)
    >
    (
    3
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    7
    x
    −
    5
    		)
    <
    (
    4
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    6
    x
    −
    3
    		)
    <
    (
    3
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    7
    x
    −
    5
    		)
    >
    (
    4
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    7
    x
    −
    5
    		)
    ≤
    (
    3
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
Question 22
22.
    • Which of the following inequations is not the same as
    • (
      −
      6
      x
      +
      4
      		)
      ≥
      (
      6
      x
      +
      6
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    42
    x
    −
    28
    		)
    ≥
    (
    54
    x
    +
    54
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    12
    x
    +
    8
    		)
    ≥
    (
    12
    x
    +
    12
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    30
    x
    −
    20
    		)
    ≤
    (
    −
    30
    x
    −
    30
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    42
    x
    −
    28
    		)
    ≤
    (
    −
    42
    x
    −
    42
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    54
    x
    +
    36
    		)
    ≥
    (
    54
    x
    +
    54
    		)
    ,
    x
    ∈
    Z
Question 23
23.
    • Find the solution set of
    • 12
      <
      (
      4
      x
      −
      8
      		)
      <
      28
      ,
      x
      ∈
      Z
  • (i)
    {6,7,8}
  • (ii)
    {7,8,9}
  • (iii)
    {5,6,7}
  • (iv)
    {8,9,10}
  • (v)
    {4,5,6}
Question 24
24.
    • Find the solution set of
    • 6
      ≤
      (
      −
      2
      x
      +
      1
      		)
      <
      18
      ,
      x
      ∈
      Z
  • (i)
    {-1,-2,-3,-4,-5,-6}
  • (ii)
    {-2,-3,-4,-5,-6,-7}
  • (iii)
    {-3,-4,-5,-6,-7,-8}
  • (iv)
    {-5,-6,-7,-8,-9,-10}
  • (v)
    {-4,-5,-6,-7,-8,-9}
Question 25
25.
    • Which of the following inequations is the same as
    • (
      −
      x
      		)
      ≤
      (
      −
      5
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    x
    		)
    >
    (
    −
    45
    x
    −
    63
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    9
    x
    		)
    <
    (
    −
    5
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    x
    		)
    <
    (
    −
    45
    x
    −
    63
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    9
    x
    		)
    >
    (
    −
    5
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    9
    x
    		)
    ≤
    (
    −
    45
    x
    −
    63
    		)
    ,
    x
    ∈
    Z
    Assignment Key
  •  1) (i)
  •  2) (iii)
  •  3) (ii)
  •  4) (ii)
  •  5) (i)
  •  6) (iv)
  •  7) (ii)
  •  8) (iii)
  •  9) (iii)
  •  10) (iii)
  •  11) (iv)
  •  12) (iv)
  •  13) (iv)
  •  14) (ii)
  •  15) (i)
  •  16) (i)
  •  17) (i)
  •  18) (iii)
  •  19) (i)
  •  20) (v)
  •  21) (v)
  •  22) (i)
  •  23) (i)
  •  24) (iii)
  •  25) (v)