EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Inequations
Grade : ICSE Grade VII
License : Non Commercial Use
Question 1
1.
    • The solution set of the inequality
    • (
      −
      2
      x
      +
      7
      		)
      >
      9
      ,
      x
      ∈
      Z
    • is
  • (i)
    {8,9,10,11,12,...}
  • (ii)
    {-2,-3,-4,-5,-6,...}
  • (iii)
    {1,2,3,4,5,...}
  • (iv)
    {0,1,2,3,4,...}
  • (v)
    {-1,-2,-3,-4,-5,...}
Question 2
2.
Which of the following statements are true?
a)
Multiplying same positive number on both sides does not change the inequality
b)
Multiplying same negative number on both sides does not change the inequality
c)
Dividing 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)
    {c,d}
  • (iv)
    {a,d,e,f}
  • (v)
    {b,f,a}
Question 3
3.
    • Identify the solution for the inequality
    • (
      −
      7
      x
      −
      14
      		)
      <
      0
      ,
      x
      ∈
      Z
  • (i)
    III
  • (ii)
    IV
  • (iii)
    I
  • (iv)
    II
Question 4
4.
    • Solve the inequation
    • (
      3
      x
      −
      9
      		)
      >
      0
      ,
      x
      ∈
      Z
  • (i)
    {3,4,5,6,7,...}
  • (ii)
    {3,2,1,0,-1,...}
  • (iii)
    {2,1,0,-1,-2,...}
  • (iv)
    {4,5,6,7,8,...}
Question 5
5.
    • Which of the following inequations is the same as
    • (
      5
      x
      +
      3
      		)
      >
      (
      8
      x
      +
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    6
    x
    −
    6
    		)
    <
    (
    8
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    6
    x
    −
    6
    		)
    >
    (
    8
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    5
    x
    +
    3
    		)
    <
    (
    9
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    6
    x
    −
    6
    		)
    >
    (
    9
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    5
    x
    +
    3
    		)
    >
    (
    9
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
Question 6
6.
    • Identify the solution for the inequality
    • (
      7
      x
      −
      56
      		)
      >
      0
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    III
  • (iii)
    II
  • (iv)
    I
Question 7
7.
    • Find the solution set for the given inequation
    • (
      9
      x
      −
      81
      		)
      >
      0
      ,
      where the replacement set is
      {7,8,9,10,11,12,13}
  • (i)
    {9,10,11,12,13}
  • (ii)
    {10,11,12,13}
  • (iii)
    {8,7,6,5,4}
  • (iv)
    {9,8,7,6,5}
  • (v)
    {10,11,12,13,14}
Question 8
8.
    • Find the solution set for the given inequation
    • (
      3
      x
      −
      3
      		)
      ≤
      0
      ,
      where the replacement set is
      {4,3,2,1,0,-1,-2}
  • (i)
    {2,3,4,5,6}
  • (ii)
    {1,0,-1,-2,-3}
  • (iii)
    {1,0,-1,-2}
  • (iv)
    {0,-1,-2,-3,-4}
  • (v)
    {1,2,3,4,5}
Question 9
9.
    • Which of the following inequations is not the same as
    • (
      −
      7
      x
      		)
      >
      (
      −
      5
      x
      +
      4
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    63
    x
    		)
    >
    (
    −
    45
    x
    +
    36
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    56
    x
    		)
    >
    (
    −
    45
    x
    +
    36
    		)
    ,
    x
    ∈
    Z
  • (iii)
    42
    x
    <
    (
    30
    x
    −
    24
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    14
    x
    		)
    >
    (
    −
    10
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    56
    x
    		)
    >
    (
    −
    40
    x
    +
    32
    		)
    ,
    x
    ∈
    Z
Question 10
10.
    • Which of the following inequations is not the same as
    • (
      −
      8
      x
      −
      8
      		)
      <
      (
      −
      4
      x
      −
      8
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    12
    x
    −
    11
    		)
    <
    (
    −
    8
    x
    −
    11
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    17
    x
    +
    1
    		)
    <
    (
    3
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    10
    x
    −
    12
    		)
    <
    (
    −
    6
    x
    −
    12
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    17
    x
    +
    1
    		)
    <
    (
    −
    13
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    x
    −
    4
    		)
    <
    (
    3
    x
    −
    4
    		)
    ,
    x
    ∈
    Z
Question 11
11.
    • The solution set of the inequality
    • (
      6
      x
      +
      8
      		)
      ≤
      6
      ,
      x
      ∈
      Z
    • is
  • (i)
    {4,5,6,7,8,...}
  • (ii)
    {0,1,2,3,4,...}
  • (iii)
    {8,9,10,11,12,...}
  • (iv)
    {-1,-2,-3,-4,-5,...}
Question 12
12.
    • Find the solution set of
    • 3
      <
      (
      −
      4
      x
      −
      3
      		)
      <
      27
      ,
      x
      ∈
      Z
  • (i)
    {-4,-5,-6,-7,-8,-9}
  • (ii)
    {-2,-3,-4,-5,-6,-7}
  • (iii)
    {-1,-2,-3,-4,-5,-6}
  • (iv)
    {0,-1,-2,-3,-4,-5}
  • (v)
    {-3,-4,-5,-6,-7,-8}
Question 13
13.
    • Find the solution set of
    • 3
      <
      (
      −
      5
      x
      +
      6
      		)
      ≤
      28
      ,
      x
      ∈
      Z
  • (i)
    {-2,-3,-4,-5,-6}
  • (ii)
    {2,1,0,-1,-2}
  • (iii)
    {0,-1,-2,-3,-4}
  • (iv)
    {-1,-2,-3,-4,-5}
  • (v)
    {1,0,-1,-2,-3}
Question 14
14.
    • Which of the following inequations is the same as
    • (
      6
      x
      +
      1
      		)
      <
      (
      x
      +
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    4
    x
    +
    10
    		)
    <
    (
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    4
    x
    +
    10
    		)
    >
    (
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    6
    x
    +
    1
    		)
    <
    (
    −
    x
    +
    11
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    6
    x
    +
    1
    		)
    >
    (
    −
    x
    +
    11
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    4
    x
    +
    10
    		)
    <
    (
    −
    x
    +
    11
    		)
    ,
    x
    ∈
    Z
Question 15
15.
    • Solve the inequation
    • (
      −
      4
      x
      		)
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    {1,2,3,4,5,...}
  • (ii)
    {0,-1,-2,-3,-4,...}
  • (iii)
    {0,1,2,3,4,...}
  • (iv)
    {-1,-2,-3,-4,-5,...}
Question 16
16.
    • Find the solution set of
    • (
      −
      6
      		)
      ≥
      (
      −
      7
      x
      −
      6
      		)
      ≥
      (
      −
      19
      		)
      ,
      x
      ∈
      Z
  • (i)
    {-1,0}
  • (ii)
    {-2,-1}
  • (iii)
    {2,3}
  • (iv)
    {1,2}
  • (v)
    {0,1}
Question 17
17.
    • Which of the following inequations is not the same as
    • (
      5
      x
      −
      5
      		)
      ≤
      (
      x
      +
      3
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    2
    x
    −
    6
    		)
    ≤
    (
    −
    6
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    10
    x
    +
    2
    		)
    ≤
    (
    6
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    10
    x
    +
    2
    		)
    ≤
    (
    6
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    10
    x
    +
    1
    		)
    ≤
    (
    6
    x
    +
    9
    		)
    ,
    x
    ∈
    Z
  • (v)
    10
    x
    ≤
    (
    6
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
Question 18
18.
    • Identify the solution for the inequality
    • (
      −
      4
      x
      −
      32
      		)
      ≥
      0
      ,
      x
      ∈
      Z
  • (i)
    I
  • (ii)
    II
  • (iii)
    III
  • (iv)
    IV
Question 19
19.
    • Which of the following inequations is not the same as
    • (
      −
      3
      x
      −
      5
      		)
      >
      (
      −
      7
      x
      −
      9
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    3
    x
    −
    5
    		)
    >
    (
    −
    x
    −
    9
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    3
    x
    −
    5
    		)
    >
    (
    −
    16
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    x
    −
    2
    		)
    >
    (
    −
    3
    x
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    5
    x
    −
    5
    		)
    >
    (
    x
    −
    9
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    4
    x
    −
    12
    		)
    >
    (
    −
    16
    		)
    ,
    x
    ∈
    Z
Question 20
20.
    • Which of the following figures represents the solution set
    • {-3,-4,-5,-6,-7,-8,...}
  • (i)
    II
  • (ii)
    I
  • (iii)
    IV
  • (iv)
    III
Question 21
21.
    • The simplified form of the inequality
    • 7
      x
      ≤
      (
      −
      2
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≥
    (
    −
    1
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≤
    (
    −
    2
    7
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    >
    (
    −
    3
    7
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    (
    −
    1
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    <
    (
    −
    3
    7
    		)
    ,
    x
    ∈
    Z
Question 22
22.
    • The simplified form of the inequality
    • (
      −
      2
      x
      −
      3
      		)
      >
      0
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    (
    −
    3
    2
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    ≤
    (
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    >
    (
    −
    1
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≥
    (
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    <
    (
    −
    1
    		)
    ,
    x
    ∈
    Z
Question 23
23.
    • Identify the solution for the inequality
    • (
      −
      4
      x
      +
      32
      		)
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    IV
  • (ii)
    II
  • (iii)
    I
  • (iv)
    III
Question 24
24.
    • Which of the following inequations is not the same as
    • (
      6
      x
      +
      9
      		)
      >
      (
      4
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    2
    x
    		)
    >
    (
    5
    x
    −
    9
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    2
    x
    +
    18
    		)
    >
    2
    ,
    x
    ∈
    Z
  • (iii)
    (
    10
    x
    +
    6
    		)
    >
    (
    8
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    2
    x
    		)
    >
    (
    −
    4
    x
    −
    16
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    7
    x
    +
    7
    		)
    >
    (
    5
    x
    −
    9
    		)
    ,
    x
    ∈
    Z
Question 25
25.
    • The solution set of the inequality
    • 7
      x
      ≥
      6
      ,
      x
      ∈
      Z
    • is
  • (i)
    {0,1,2,3,4,...}
  • (ii)
    {-1,-2,-3,-4,-5,...}
  • (iii)
    {1,2,3,4,5,...}
  • (iv)
    {0,-1,-2,-3,-4,...}
    Assignment Key
  •  1) (ii)
  •  2) (iv)
  •  3) (ii)
  •  4) (iv)
  •  5) (iv)
  •  6) (ii)
  •  7) (ii)
  •  8) (iii)
  •  9) (ii)
  •  10) (ii)
  •  11) (iv)
  •  12) (ii)
  •  13) (iii)
  •  14) (v)
  •  15) (iii)
  •  16) (v)
  •  17) (ii)
  •  18) (iii)
  •  19) (ii)
  •  20) (iii)
  •  21) (ii)
  •  22) (i)
  •  23) (i)
  •  24) (i)
  •  25) (iii)