EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Inequations
Grade : ICSE Grade VIII
License : Non Commercial Use
Question 1
1.
    • Which of the following inequations is not the same as
    • (
      −
      9
      x
      −
      8
      		)
      >
      (
      3
      x
      −
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    5
    x
    −
    11
    		)
    >
    (
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    6
    x
    −
    6
    		)
    >
    (
    6
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    12
    x
    −
    11
    		)
    >
    (
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    4
    x
    −
    8
    		)
    >
    (
    8
    x
    −
    1
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    5
    x
    −
    11
    		)
    >
    (
    7
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
Question 2
2.
    • Which of the following inequations is not the same as
    • (
      x
      +
      6
      		)
      ≥
      (
      −
      6
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    6
    x
    +
    15
    		)
    ≥
    (
    −
    13
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    6
    x
    		)
    ≥
    (
    −
    13
    x
    −
    13
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    6
    x
    +
    9
    		)
    ≥
    (
    −
    13
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    8
    x
    +
    1
    		)
    ≥
    (
    x
    −
    12
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    6
    x
    +
    15
    		)
    ≥
    (
    −
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
Question 3
3.
    • Which of the following inequations is not the same as
    • (
      −
      9
      x
      −
      1
      		)
      >
      (
      −
      3
      x
      −
      6
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    12
    x
    +
    3
    		)
    >
    (
    −
    6
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    6
    x
    −
    9
    		)
    >
    (
    −
    14
    		)
    ,
    x
    ∈
    Z
  • (iii)
    1
    >
    (
    6
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    7
    x
    +
    3
    		)
    >
    (
    −
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    1
    >
    (
    −
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
Question 4
4.
    • The simplified form of the inequality
    • (
      4
      x
      +
      6
      		)
      <
      (
      6
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    >
    3
    ,
    x
    ∈
    Z
  • (ii)
    x
    <
    3
    ,
    x
    ∈
    Z
  • (iii)
    x
    >
    5
    2
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    2
    ,
    x
    ∈
    Z
  • (v)
    x
    ≥
    2
    ,
    x
    ∈
    Z
Question 5
5.
    • Find the solution set of
    • 16
      <
      (
      7
      x
      −
      4
      		)
      <
      29
      ,
      x
      ∈
      Z
  • (i)
    {3,4}
  • (ii)
    {5,6}
  • (iii)
    {4,5}
  • (iv)
    {2,3}
  • (v)
    {1,2}
Question 6
6.
    • Which of the following figures represents the solution set
    • {-9,-8,-7,-6,-5,-4,...}
  • (i)
    II
  • (ii)
    III
  • (iii)
    IV
  • (iv)
    I
Question 7
7.
    • The solution set of the inequality
    • (
      2
      x
      −
      4
      		)
      <
      6
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-2,-3,-4,-5,-6,...}
  • (ii)
    {6,7,8,9,10,...}
  • (iii)
    {4,3,2,1,0,...}
  • (iv)
    {0,1,2,3,4,...}
  • (v)
    {5,6,7,8,9,...}
Question 8
8.
    • Which of the following inequations is not the same as
    • (
      −
      4
      x
      −
      3
      		)
      >
      (
      9
      x
      −
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    8
    x
    −
    6
    		)
    >
    (
    18
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    4
    x
    +
    3
    		)
    <
    (
    −
    9
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    8
    x
    +
    6
    		)
    <
    (
    −
    18
    x
    +
    18
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    28
    x
    −
    21
    		)
    >
    (
    63
    x
    −
    63
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    28
    x
    −
    21
    		)
    >
    (
    18
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
Question 9
9.
    • Which of the following inequations is the same as
    • (
      4
      x
      +
      4
      		)
      <
      (
      −
      x
      −
      8
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    4
    x
    +
    4
    		)
    >
    (
    −
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    x
    +
    10
    		)
    <
    (
    −
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    x
    +
    10
    		)
    >
    (
    −
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    x
    +
    10
    		)
    <
    (
    −
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    4
    x
    +
    4
    		)
    <
    (
    −
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
Question 10
10.
    • Solve the inequation
    • (
      −
      8
      x
      −
      24
      		)
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    {-2,-1,0,1,2,...}
  • (ii)
    {-3,-2,-1,0,1,...}
  • (iii)
    {-3,-4,-5,-6,-7,...}
  • (iv)
    {-4,-5,-6,-7,-8,...}
Question 11
11.
    • Find the solution set of
    • (
      −
      6
      		)
      ≥
      (
      −
      5
      x
      +
      1
      		)
      >
      (
      −
      21
      		)
      ,
      x
      ∈
      Z
  • (i)
    {1,2,3}
  • (ii)
    {3,4,5}
  • (iii)
    {0,1,2}
  • (iv)
    {2,3,4}
  • (v)
    {4,5,6}
Question 12
12.
    • Which of the following inequations is the same as
    • (
      4
      x
      +
      6
      		)
      ≤
      (
      −
      4
      x
      +
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    4
    x
    +
    6
    		)
    <
    (
    −
    8
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    4
    x
    +
    6
    		)
    >
    (
    −
    8
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    2
    		)
    ≤
    (
    −
    8
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    2
    		)
    <
    (
    −
    4
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    2
    		)
    >
    (
    −
    4
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
Question 13
13.
    • Find the solution set of
    • (
      −
      5
      		)
      <
      (
      −
      6
      x
      +
      2
      		)
      ≤
      21
      ,
      x
      ∈
      Z
  • (i)
    {1,0,-1,-2,-3}
  • (ii)
    {3,2,1,0,-1}
  • (iii)
    {0,-1,-2,-3,-4}
  • (iv)
    {2,1,0,-1,-2}
  • (v)
    {-1,-2,-3,-4,-5}
Question 14
14.
    • Which of the following inequations is the same as
    • (
      −
      4
      x
      +
      5
      		)
      ≥
      (
      −
      2
      x
      −
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    7
    x
    +
    2
    		)
    ≥
    (
    −
    5
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    4
    x
    +
    5
    		)
    >
    (
    −
    5
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    7
    x
    +
    2
    		)
    >
    (
    −
    2
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    7
    x
    +
    2
    		)
    <
    (
    −
    2
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    4
    x
    +
    5
    		)
    <
    (
    −
    5
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
Question 15
15.
    • Identify the solution for the inequality
    • 10
      ≥
      (
      7
      x
      −
      1
      		)
      >
      (
      −
      17
      		)
      ,
      x
      ∈
      Z
  • (i)
    I
  • (ii)
    II
  • (iii)
    III
  • (iv)
    IV
Question 16
16.
    • Identify the solution for the inequality
    • (
      −
      10
      		)
      ≥
      (
      −
      5
      x
      −
      6
      		)
      ≥
      (
      −
      25
      		)
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    I
  • (iii)
    II
  • (iv)
    III
Question 17
17.
Which of the following statements are true?
a)
Multiplying same positive number on both sides does not change the inequality
b)
Adding same number on both sides does not change the inequality
c)
Multiplying same negative number on both sides does not change the inequality
d)
Dividing same negative number on both sides does not change the inequality
e)
Subtracting same number on both sides does not change the inequality
f)
Dividing same positive number on both sides does not change the inequality
  • (i)
    {c,a}
  • (ii)
    {a,b,e,f}
  • (iii)
    {c,f,a}
  • (iv)
    {c,d,e}
  • (v)
    {d,b}
Question 18
18.
    • Find the solution set for the given inequation
    • (
      −
      8
      x
      +
      32
      		)
      ≥
      0
      ,
      where the replacement set is
      {7,6,5,4,3,2,1}
  • (i)
    {4,5,6,7,8}
  • (ii)
    {5,6,7,8,9}
  • (iii)
    {4,3,2,1}
  • (iv)
    {4,3,2,1,0}
  • (v)
    {3,2,1,0,-1}
Question 19
19.
    • The solution set of the inequality
    • (
      −
      4
      x
      −
      1
      		)
      <
      (
      3
      x
      +
      7
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-2,-3,-4,-5,-6,...}
  • (ii)
    {1,0,-1,-2,-3,...}
  • (iii)
    {-1,0,1,2,3,...}
  • (iv)
    {0,-1,-2,-3,-4,...}
Question 20
20.
    • Which of the following inequations is not the same as
    • (
      3
      x
      +
      6
      		)
      <
      (
      7
      x
      −
      4
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    x
    +
    11
    		)
    <
    (
    5
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    5
    x
    −
    2
    		)
    <
    (
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    8
    <
    (
    4
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    x
    +
    6
    		)
    <
    (
    3
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    5
    x
    −
    2
    		)
    <
    (
    9
    x
    −
    12
    		)
    ,
    x
    ∈
    Z
Question 21
21.
    • Which of the following inequations is the same as
    • (
      2
      x
      −
      6
      		)
      ≤
      (
      −
      5
      x
      −
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    11
    x
    −
    5
    		)
    <
    (
    −
    5
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    11
    x
    −
    5
    		)
    ≤
    (
    4
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    2
    x
    −
    6
    		)
    >
    (
    4
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    11
    x
    −
    5
    		)
    >
    (
    −
    5
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    2
    x
    −
    6
    		)
    <
    (
    4
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
Question 22
22.
    • Which of the following inequations is the same as
    • (
      x
      −
      3
      		)
      >
      (
      −
      2
      x
      +
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    x
    −
    3
    		)
    >
    (
    −
    9
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    x
    −
    3
    		)
    <
    (
    −
    9
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    6
    x
    −
    4
    		)
    <
    (
    −
    2
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    6
    x
    −
    4
    		)
    >
    (
    −
    2
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    6
    x
    −
    4
    		)
    >
    (
    −
    9
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
Question 23
23.
    • Identify the solution for the inequality
    • (
      −
      9
      x
      +
      27
      		)
      ≤
      0
      ,
      x
      ∈
      N
  • (i)
    III
  • (ii)
    II
  • (iii)
    I
  • (iv)
    IV
Question 24
24.
    • The simplified form of the inequality
    • (
      −
      4
      x
      −
      6
      		)
      ≤
      (
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≥
    (
    −
    7
    5
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    (
    −
    6
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    <
    (
    −
    6
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≥
    (
    −
    8
    5
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≤
    (
    −
    8
    5
    		)
    ,
    x
    ∈
    Z
Question 25
25.
    • Which of the following inequations is not the same as
    • (
      −
      9
      x
      −
      9
      		)
      <
      (
      −
      5
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    54
    x
    +
    54
    		)
    <
    (
    −
    35
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    18
    x
    +
    18
    		)
    >
    (
    10
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    63
    x
    −
    63
    		)
    <
    (
    −
    35
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    27
    x
    −
    27
    		)
    <
    (
    −
    15
    x
    +
    3
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    54
    x
    +
    54
    		)
    >
    (
    30
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
    Assignment Key
  •  1) (i)
  •  2) (i)
  •  3) (v)
  •  4) (iii)
  •  5) (i)
  •  6) (iv)
  •  7) (iii)
  •  8) (v)
  •  9) (iv)
  •  10) (ii)
  •  11) (iv)
  •  12) (iii)
  •  13) (i)
  •  14) (i)
  •  15) (ii)
  •  16) (iii)
  •  17) (ii)
  •  18) (iii)
  •  19) (iii)
  •  20) (ii)
  •  21) (ii)
  •  22) (v)
  •  23) (iv)
  •  24) (i)
  •  25) (i)