EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Inequations
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
    • The simplified form of the inequality
    • (
      3
      x
      +
      7
      		)
      ≥
      (
      −
      9
      x
      +
      4
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    >
    (
    −
    1
    3
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    (
    −
    1
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    (
    −
    1
    6
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    <
    (
    −
    1
    3
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≤
    (
    −
    1
    6
    		)
    ,
    x
    ∈
    Z
Question 2
2.
    • The solution set of the inequality
    • (
      3
      x
      −
      2
      		)
      <
      (
      8
      x
      −
      6
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {0,-1,-2,-3,-4,...}
  • (ii)
    {2,3,4,5,6,...}
  • (iii)
    {-1,-2,-3,-4,-5,...}
  • (iv)
    {1,2,3,4,5,...}
Question 3
3.
    • Which of the following figures represents the solution set
    • {8,7,6,5,4,3,...}
  • (i)
    III
  • (ii)
    II
  • (iii)
    IV
  • (iv)
    I
Question 4
4.
    • Solve the inequation
    • (
      x
      −
      8
      		)
      <
      0
      ,
      x
      ∈
      Z
  • (i)
    {9,10,11,12,13,...}
  • (ii)
    {8,9,10,11,12,...}
  • (iii)
    {8,7,6,5,4,...}
  • (iv)
    {7,6,5,4,3,...}
Question 5
5.
    • The solution set of the inequality
    • (
      6
      x
      +
      9
      		)
      ≤
      (
      8
      x
      −
      8
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-1,0,1,2,3,...}
  • (ii)
    {0,-1,-2,-3,-4,...}
  • (iii)
    {8,7,6,5,4,...}
  • (iv)
    {9,10,11,12,13,...}
Question 6
6.
    • Which of the following inequations is the same as
    • (
      −
      8
      x
      −
      5
      		)
      <
      (
      −
      7
      x
      −
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    8
    x
    −
    5
    		)
    >
    (
    −
    63
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    72
    x
    −
    45
    		)
    >
    (
    −
    7
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    72
    x
    −
    45
    		)
    <
    (
    −
    7
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    72
    x
    −
    45
    		)
    <
    (
    −
    63
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    8
    x
    −
    5
    		)
    <
    (
    −
    63
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
Question 7
7.
    • Find the solution set for the given inequation
    • (
      4
      x
      −
      20
      		)
      ≤
      0
      ,
      where the replacement set is
      {8,7,6,5,4,3,2}
  • (i)
    {4,3,2,1,0}
  • (ii)
    {6,7,8,9,10}
  • (iii)
    {5,4,3,2}
  • (iv)
    {5,4,3,2,1}
  • (v)
    {5,6,7,8,9}
Question 8
8.
    • Find the solution set of
    • 7
      ≤
      (
      7
      x
      −
      5
      		)
      <
      20
      ,
      x
      ∈
      Z
  • (i)
    {1,2}
  • (ii)
    {3,4}
  • (iii)
    {2,3}
  • (iv)
    {4,5}
  • (v)
    {0,1}
Question 9
9.
    • Solve the inequation
    		•
      9
      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 10
10.
    • Which of the following inequations is the same as
    • (
      2
      x
      +
      2
      		)
      ≤
      (
      x
      +
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    4
    x
    +
    1
    		)
    <
    (
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    4
    x
    +
    1
    		)
    >
    (
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    2
    x
    +
    2
    		)
    >
    (
    −
    5
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    4
    x
    +
    1
    		)
    ≤
    (
    −
    5
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    2
    x
    +
    2
    		)
    <
    (
    −
    5
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
Question 11
11.
    • Which of the following inequations is not the same as
    • (
      −
      5
      x
      +
      1
      		)
      >
      (
      −
      6
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    2
    x
    −
    5
    		)
    >
    (
    −
    3
    x
    −
    5
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    3
    x
    +
    6
    		)
    >
    (
    −
    4
    x
    +
    6
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    10
    x
    −
    8
    		)
    >
    (
    −
    11
    x
    −
    8
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    7
    x
    −
    6
    		)
    >
    (
    −
    8
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    2
    x
    −
    5
    		)
    >
    (
    −
    4
    x
    +
    6
    		)
    ,
    x
    ∈
    Z
Question 12
12.
    • Which of the following inequations is not the same as
    • (
      −
      x
      +
      1
      		)
      ≥
      (
      −
      3
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    3
    x
    −
    3
    		)
    ≤
    (
    9
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    3
    x
    −
    3
    		)
    ≥
    (
    −
    6
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    2
    x
    +
    2
    		)
    ≥
    (
    −
    6
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    x
    +
    1
    		)
    ≥
    (
    −
    3
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    5
    x
    +
    5
    		)
    ≥
    (
    −
    15
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
Question 13
13.
    • The simplified form of the inequality
    • (
      7
      x
      −
      7
      		)
      <
      (
      −
      9
      x
      −
      4
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    3
    16
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    1
    4
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≤
    1
    4
    ,
    x
    ∈
    Z
  • (iv)
    x
    <
    1
    8
    ,
    x
    ∈
    Z
  • (v)
    x
    >
    1
    8
    ,
    x
    ∈
    Z
Question 14
14.
    • Which of the following inequations is not the same as
    • (
      −
      8
      x
      −
      3
      		)
      ≤
      (
      7
      x
      −
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    72
    x
    −
    27
    		)
    ≤
    (
    63
    x
    −
    45
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    16
    x
    −
    6
    		)
    ≤
    (
    14
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    32
    x
    −
    12
    		)
    ≤
    (
    28
    x
    −
    20
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    32
    x
    −
    12
    		)
    ≤
    (
    −
    28
    x
    +
    20
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    32
    x
    +
    12
    		)
    ≥
    (
    −
    28
    x
    +
    20
    		)
    ,
    x
    ∈
    Z
Question 15
15.
    • Which of the following inequations is the same as
    • (
      −
      8
      x
      −
      4
      		)
      >
      (
      −
      x
      −
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    8
    x
    −
    4
    		)
    >
    (
    −
    7
    x
    −
    14
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    56
    x
    −
    28
    		)
    <
    (
    −
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    56
    x
    −
    28
    		)
    >
    (
    −
    7
    x
    −
    14
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    8
    x
    −
    4
    		)
    <
    (
    −
    7
    x
    −
    14
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    56
    x
    −
    28
    		)
    >
    (
    −
    x
    −
    2
    		)
    ,
    x
    ∈
    Z
Question 16
16.
    • The solution set of the inequality
    • (
      2
      x
      +
      5
      		)
      ≤
      5
      ,
      x
      ∈
      Z
    • is
  • (i)
    {0,-1,-2,-3,-4,...}
  • (ii)
    {1,0,-1,-2,-3,...}
  • (iii)
    {0,1,2,3,4,...}
  • (iv)
    {1,2,3,4,5,...}
Question 17
17.
    • The simplified form of the inequality
    • (
      6
      x
      −
      7
      		)
      ≥
      (
      −
      7
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    (
    −
    1
    6
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    (
    −
    1
    6
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    1
    6
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    1
    6
    ,
    x
    ∈
    Z
  • (v)
    x
    ≥
    0
    ,
    x
    ∈
    Z
Question 18
18.
    • Find the solution set of
    • (
      −
      3
      		)
      ≤
      (
      5
      x
      +
      3
      		)
      ≤
      12
      ,
      x
      ∈
      Z
  • (i)
    {1,2,3}
  • (ii)
    {0,1,2}
  • (iii)
    {-3,-2,-1}
  • (iv)
    {-1,0,1}
  • (v)
    {-2,-1,0}
Question 19
19.
    • Find the solution set of
    • 2
      <
      (
      −
      5
      x
      +
      5
      		)
      <
      27
      ,
      x
      ∈
      Z
  • (i)
    {1,0,-1,-2,-3}
  • (ii)
    {-1,-2,-3,-4,-5}
  • (iii)
    {-2,-3,-4,-5,-6}
  • (iv)
    {0,-1,-2,-3,-4}
  • (v)
    {2,1,0,-1,-2}
Question 20
20.
    • Find the solution set of
    • 3
      <
      (
      −
      2
      x
      −
      7
      		)
      ≤
      15
      ,
      x
      ∈
      Z
  • (i)
    {-4,-5,-6,-7,-8,-9}
  • (ii)
    {-6,-7,-8,-9,-10,-11}
  • (iii)
    {-7,-8,-9,-10,-11,-12}
  • (iv)
    {-8,-9,-10,-11,-12,-13}
  • (v)
    {-5,-6,-7,-8,-9,-10}
Question 21
21.
    • Which of the following inequations is the same as
    • (
      x
      +
      6
      		)
      >
      (
      6
      x
      −
      4
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    5
    x
    +
    15
    		)
    >
    (
    6
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    x
    +
    6
    		)
    >
    (
    10
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    x
    +
    6
    		)
    <
    (
    10
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    5
    x
    +
    15
    		)
    >
    (
    10
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    5
    x
    +
    15
    		)
    <
    (
    6
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
Question 22
22.
    • Find the solution set for the given inequation
    • (
      x
      +
      8
      		)
      >
      0
      ,
      where the replacement set is
      {-10,-9,-8,-7,-6,-5,-4}
  • (i)
    {-7,-6,-5,-4}
  • (ii)
    {-7,-6,-5,-4,-3}
  • (iii)
    {-8,-7,-6,-5,-4}
  • (iv)
    {-9,-10,-11,-12,-13}
  • (v)
    {-8,-9,-10,-11,-12}
Question 23
23.
    • Which of the following inequations is not the same as
    • (
      2
      x
      +
      9
      		)
      ≥
      (
      −
      4
      x
      +
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    3
    x
    +
    5
    		)
    ≥
    (
    −
    3
    x
    +
    13
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    3
    x
    +
    17
    		)
    ≥
    (
    −
    3
    x
    +
    13
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    5
    x
    +
    9
    		)
    ≥
    (
    −
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    3
    x
    +
    5
    		)
    ≥
    (
    −
    3
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    4
    x
    +
    12
    		)
    ≥
    (
    −
    10
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
Question 24
24.
    • The simplified form of the inequality
    • (
      −
      8
      x
      +
      7
      		)
      <
      (
      −
      5
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    >
    13
    8
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≥
    11
    8
    ,
    x
    ∈
    Z
  • (iii)
    x
    <
    13
    8
    ,
    x
    ∈
    Z
  • (iv)
    x
    >
    3
    2
    ,
    x
    ∈
    Z
  • (v)
    x
    ≤
    11
    8
    ,
    x
    ∈
    Z
Question 25
25.
Which of the following statements are true?
a)
Multiplying same positive number on both sides does not change the inequality
b)
Dividing same negative number on both sides does not change the inequality
c)
Multiplying same negative number on both sides does not change the inequality
d)
Subtracting same number on both sides does not change the inequality
e)
Dividing same positive number on both sides does not change the inequality
f)
Adding same number on both sides does not change the inequality
  • (i)
    {b,c,e}
  • (ii)
    {b,a}
  • (iii)
    {a,d,e,f}
  • (iv)
    {b,f,a}
  • (v)
    {c,d}
    Assignment Key
  •  1) (ii)
  •  2) (iv)
  •  3) (iii)
  •  4) (iv)
  •  5) (iv)
  •  6) (iv)
  •  7) (iii)
  •  8) (iii)
  •  9) (iv)
  •  10) (iv)
  •  11) (v)
  •  12) (ii)
  •  13) (i)
  •  14) (iv)
  •  15) (iii)
  •  16) (i)
  •  17) (v)
  •  18) (iv)
  •  19) (iv)
  •  20) (ii)
  •  21) (iv)
  •  22) (i)
  •  23) (i)
  •  24) (iv)
  •  25) (iii)