EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Inequations
Grade : ICSE Grade VIII
License : Non Commercial Use
Question 1
1.
    • Identify the solution for the inequality
    • (
      −
      7
      x
      		)
      ≤
      0
      ,
      x
      ∈
      N
  • (i)
    III
  • (ii)
    II
  • (iii)
    I
  • (iv)
    IV
Question 2
2.
    • The simplified form of the inequality
    • (
      6
      x
      −
      6
      		)
      <
      (
      −
      5
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≤
    1
    3
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    1
    3
    ,
    x
    ∈
    Z
  • (iii)
    x
    >
    0
    ,
    x
    ∈
    Z
  • (iv)
    x
    <
    0
    ,
    x
    ∈
    Z
  • (v)
    x
    <
    1
    6
    ,
    x
    ∈
    Z
Question 3
3.
Which of the following statements are true?
a)
Subtracting same number on both sides does not change the inequality
b)
Multiplying same negative number on both sides does not change the inequality
c)
Adding same number on both sides does not change the inequality
d)
Dividing same negative number on both sides does not change the inequality
e)
Multiplying same positive number on both sides does not change the inequality
f)
Dividing same positive number on both sides does not change the inequality
  • (i)
    {b,f,a}
  • (ii)
    {b,d,e}
  • (iii)
    {d,c}
  • (iv)
    {b,a}
  • (v)
    {a,c,e,f}
Question 4
4.
    • Solve the inequation
    • (
      −
      x
      −
      9
      		)
      <
      0
      ,
      x
      ∈
      Z
  • (i)
    {-9,-10,-11,-12,-13,...}
  • (ii)
    {-10,-11,-12,-13,-14,...}
  • (iii)
    {-8,-7,-6,-5,-4,...}
  • (iv)
    {-9,-8,-7,-6,-5,...}
Question 5
5.
    • Which of the following inequations is not the same as
    • (
      −
      6
      x
      		)
      >
      (
      −
      3
      x
      +
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    3
    x
    +
    9
    		)
    >
    18
    ,
    x
    ∈
    Z
  • (ii)
    (
    2
    x
    +
    9
    		)
    >
    (
    5
    x
    +
    18
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    9
    x
    +
    4
    		)
    >
    (
    −
    6
    x
    +
    13
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    5
    x
    +
    3
    		)
    >
    (
    −
    2
    x
    +
    12
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    9
    x
    +
    4
    		)
    >
    18
    ,
    x
    ∈
    Z
Question 6
6.
    • The solution set of the inequality
    • (
      5
      x
      +
      4
      		)
      ≤
      (
      −
      4
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-2,-1,0,1,2,...}
  • (ii)
    {0,-1,-2,-3,-4,...}
  • (iii)
    {-2,-3,-4,-5,-6,...}
  • (iv)
    {-1,0,1,2,3,...}
Question 7
7.
Which of the following is not an inequation?
  • (i)
    (
    8
    x
    −
    5
    		)
    >
    (
    4
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    2
    x
    −
    6
    		)
    ≥
    (
    −
    4
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    2
    x
    +
    7
    		)
    ≤
    (
    −
    3
    x
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    x
    +
    4
    		)
    =
    (
    7
    x
    −
    5
    		)
  • (v)
    (
    8
    x
    +
    8
    		)
    <
    (
    3
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
Question 8
8.
    • Which of the following inequations is the same as
    • 6
      x
      ≤
      (
      x
      −
      3
      		)
      ,
      x
      ∈
      Z
  • (i)
    6
    x
    >
    (
    5
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (ii)
    30
    x
    ≤
    (
    5
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (iii)
    6
    x
    <
    (
    5
    x
    −
    15
    		)
    ,
    x
    ∈
    Z
  • (iv)
    30
    x
    >
    (
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (v)
    30
    x
    <
    (
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
Question 9
9.
    • Solve the inequation
    • (
      −
      x
      +
      8
      		)
      >
      0
      ,
      x
      ∈
      Z
  • (i)
    {7,6,5,4,3,...}
  • (ii)
    {8,9,10,11,12,...}
  • (iii)
    {8,7,6,5,4,...}
  • (iv)
    {9,10,11,12,13,...}
Question 10
10.
    • The solution set of the inequality
    • (
      6
      x
      +
      1
      		)
      ≥
      (
      3
      x
      −
      9
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-4,-5,-6,-7,-8,...}
  • (ii)
    {-1,-2,-3,-4,-5,...}
  • (iii)
    {0,-1,-2,-3,-4,...}
  • (iv)
    {-3,-2,-1,0,1,...}
Question 11
11.
    • Solve the inequation
    		•
      7
      x
      ≥
      0
      ,
      x
      ∈
      Z
  • (i)
    {0,1,2,3,4,...}
  • (ii)
    {-1,-2,-3,-4,-5,...}
  • (iii)
    {1,2,3,4,5,...}
  • (iv)
    {0,-1,-2,-3,-4,...}
Question 12
12.
    • Find the solution set of
    • 4
      ≤
      (
      9
      x
      −
      6
      		)
      ≤
      15
      ,
      x
      ∈
      Z
  • (i)
    {4}
  • (ii)
    {2}
  • (iii)
    {1}
  • (iv)
    {3}
  • (v)
    {0}
Question 13
13.
    • Which of the following inequations is not the same as
    • (
      −
      8
      x
      +
      8
      		)
      <
      (
      −
      6
      x
      −
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    14
    x
    +
    15
    		)
    <
    (
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    15
    x
    +
    10
    		)
    <
    (
    −
    13
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    14
    x
    +
    15
    		)
    <
    (
    −
    12
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    6
    x
    +
    11
    		)
    <
    (
    −
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    x
    +
    3
    		)
    <
    (
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
Question 14
14.
    • The solution set of the inequality
    • (
      −
      3
      x
      −
      8
      		)
      <
      7
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-2,-1,0,1,2,...}
  • (ii)
    {-5,-6,-7,-8,-9,...}
  • (iii)
    {-3,-2,-1,0,1,...}
  • (iv)
    {-4,-3,-2,-1,0,...}
  • (v)
    {-6,-7,-8,-9,-10,...}
Question 15
15.
    • Find the solution set of
    • (
      −
      7
      		)
      ≥
      (
      −
      8
      x
      −
      2
      		)
      >
      (
      −
      19
      		)
      ,
      x
      ∈
      Z
  • (i)
    {-1,0}
  • (ii)
    {3,4}
  • (iii)
    {1,2}
  • (iv)
    {0,1}
  • (v)
    {2,3}
Question 16
16.
    • Identify the solution for the inequality
    • 8
      ≤
      (
      8
      x
      +
      7
      		)
      <
      20
      ,
      x
      ∈
      Z
  • (i)
    III
  • (ii)
    II
  • (iii)
    I
  • (iv)
    IV
Question 17
17.
    • Identify the solution for the inequality
    • (
      −
      x
      +
      3
      		)
      >
      0
      ,
      x
      ∈
      N
  • (i)
    III
  • (ii)
    IV
  • (iii)
    II
  • (iv)
    I
Question 18
18.
    • Find the solution set for the given inequation
    • (
      8
      x
      −
      8
      		)
      <
      0
      ,
      where the replacement set is
      {3,2,1,0,-1,-2,-3}
  • (i)
    {0,-1,-2,-3}
  • (ii)
    {0,-1,-2,-3,-4}
  • (iii)
    {2,3,4,5,6}
  • (iv)
    {1,0,-1,-2,-3}
  • (v)
    {1,2,3,4,5}
Question 19
19.
    • Which of the following inequations is not the same as
    • (
      −
      5
      x
      −
      8
      		)
      ≤
      (
      −
      6
      x
      −
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    10
    x
    +
    16
    		)
    ≥
    (
    12
    x
    +
    4
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    5
    x
    −
    8
    		)
    ≤
    (
    −
    6
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    20
    x
    −
    32
    		)
    ≤
    (
    −
    24
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    5
    x
    −
    8
    		)
    ≤
    (
    54
    x
    +
    18
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    45
    x
    +
    72
    		)
    ≥
    (
    54
    x
    +
    18
    		)
    ,
    x
    ∈
    Z
Question 20
20.
    • Find the solution set of given inequality
    • (
      −
      2
      x
      		)
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    {0,1,2,3,...}
  • (ii)
    {1,2,3,4,...}
  • (iii)
    {0,-1,-2,-3,...}
  • (iv)
    {-1,-2,-3,-4,...}
Question 21
21.
Which of the following is not an inequation?
  • (i)
    (
    −
    x
    +
    8
    		)
    ≤
    8
    ,
    x
    ∈
    Z
  • (ii)
    (
    8
    x
    +
    8
    		)
    ≥
    (
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    2
    x
    +
    4
    		)
    =
    6
  • (iv)
    (
    −
    6
    x
    +
    3
    		)
    >
    (
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    3
    x
    +
    6
    		)
    <
    6
    ,
    x
    ∈
    Z
Question 22
22.
    • Identify the solution for the inequality
    • (
      −
      2
      		)
      ≥
      (
      −
      3
      x
      −
      6
      		)
      >
      (
      −
      19
      		)
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    I
  • (iii)
    III
  • (iv)
    II
Question 23
23.
    • The simplified form of the inequality
    • (
      −
      9
      x
      +
      8
      		)
      ≤
      (
      −
      5
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    14
    9
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≤
    4
    3
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    4
    3
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≥
    13
    9
    ,
    x
    ∈
    Z
  • (v)
    x
    >
    14
    9
    ,
    x
    ∈
    Z
Question 24
24.
    • Which of the following inequations is not the same as
    • (
      6
      x
      −
      6
      		)
      ≤
      (
      9
      x
      +
      3
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    8
    x
    −
    14
    		)
    ≤
    (
    10
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    8
    x
    −
    14
    		)
    ≤
    (
    11
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    10
    x
    −
    4
    		)
    ≤
    (
    13
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    x
    +
    1
    		)
    ≤
    (
    2
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
  • (v)
    7
    x
    ≤
    (
    10
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
Question 25
25.
    • Which of the following inequations is not the same as
    • (
      4
      x
      −
      1
      		)
      ≥
      (
      3
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    28
    x
    +
    7
    		)
    ≤
    (
    −
    21
    x
    +
    49
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    24
    x
    +
    6
    		)
    ≤
    (
    −
    18
    x
    +
    42
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    36
    x
    −
    9
    		)
    ≥
    (
    27
    x
    −
    63
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    4
    x
    +
    1
    		)
    ≤
    (
    −
    3
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    4
    x
    +
    1
    		)
    ≥
    (
    −
    21
    x
    +
    49
    		)
    ,
    x
    ∈
    Z
    Assignment Key
  •  1) (ii)
  •  2) (v)
  •  3) (v)
  •  4) (iii)
  •  5) (v)
  •  6) (iii)
  •  7) (iv)
  •  8) (ii)
  •  9) (i)
  •  10) (iv)
  •  11) (i)
  •  12) (ii)
  •  13) (i)
  •  14) (iv)
  •  15) (iii)
  •  16) (ii)
  •  17) (i)
  •  18) (i)
  •  19) (iv)
  •  20) (i)
  •  21) (iii)
  •  22) (iv)
  •  23) (iv)
  •  24) (i)
  •  25) (v)