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
    • (
      −
      6
      x
      +
      9
      		)
      <
      (
      4
      x
      −
      2
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {2,3,4,5,6,...}
  • (ii)
    {1,0,-1,-2,-3,...}
  • (iii)
    {1,2,3,4,5,...}
  • (iv)
    {0,1,2,3,4,...}
Question 2
2.
    • Which of the following inequations is the same as
    • (
      −
      x
      +
      9
      		)
      >
      (
      −
      6
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    5
    x
    +
    45
    		)
    >
    (
    −
    30
    x
    −
    35
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    5
    x
    +
    45
    		)
    <
    (
    −
    6
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    x
    +
    9
    		)
    >
    (
    −
    30
    x
    −
    35
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    x
    +
    9
    		)
    <
    (
    −
    30
    x
    −
    35
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    5
    x
    +
    45
    		)
    >
    (
    −
    6
    x
    −
    7
    		)
    ,
    x
    ∈
    Z
Question 3
3.
    • Find the solution set of
    • 4
      ≤
      6
      x
      <
      18
      ,
      x
      ∈
      Z
  • (i)
    {3,4}
  • (ii)
    {1,2}
  • (iii)
    {2,3}
  • (iv)
    {-1,0}
  • (v)
    {0,1}
Question 4
4.
    • Solve the inequation
    • (
      −
      2
      x
      		)
      <
      0
      ,
      x
      ∈
      Z
  • (i)
    {-1,-2,-3,-4,-5,...}
  • (ii)
    {1,2,3,4,5,...}
  • (iii)
    {0,1,2,3,4,...}
  • (iv)
    {0,-1,-2,-3,-4,...}
Question 5
5.
Which of the following is an inequation?
  • (i)
    9
  • (ii)
    (
    −
    5
    x
    −
    3
    		)
    <
    0
    ,
    x
    ∈
    Z
  • (iii)
    (
    2
    x
    +
    6
    		)
  • (iv)
    (
    x
    +
    2
    		)
    =
    0
Question 6
6.
    • Find the solution set for the given inequation
    • (
      −
      4
      x
      +
      36
      		)
      <
      0
      ,
      where the replacement set is
      {7,8,9,10,11,12,13}
  • (i)
    {9,10,11,12,13}
  • (ii)
    {8,7,6,5,4}
  • (iii)
    {10,11,12,13}
  • (iv)
    {10,11,12,13,14}
  • (v)
    {9,8,7,6,5}
Question 7
7.
    • The simplified form of the inequality
    • (
      −
      3
      x
      −
      2
      		)
      >
      3
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    (
    −
    5
    3
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    (
    −
    4
    3
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    (
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    (
    −
    2
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    <
    (
    −
    4
    3
    		)
    ,
    x
    ∈
    Z
Question 8
8.
    • The simplified form of the inequality
    • (
      −
      3
      x
      +
      1
      		)
      ≤
      (
      −
      8
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    ≤
    1
    5
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    (
    −
    1
    5
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    1
    5
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    0
    ,
    x
    ∈
    Z
  • (v)
    x
    <
    (
    −
    1
    5
    		)
    ,
    x
    ∈
    Z
Question 9
9.
Which of the following is not an inequation?
  • (i)
    (
    −
    x
    +
    6
    		)
    ≤
    (
    −
    7
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    2
    x
    +
    4
    		)
    <
    (
    −
    1
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    5
    x
    +
    1
    		)
    ≥
    (
    −
    6
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    8
    x
    −
    6
    		)
    >
    0
    ,
    x
    ∈
    Z
  • (v)
    (
    6
    x
    −
    1
    		)
    =
    3
Question 10
10.
    • The solution set of the inequality
    • (
      −
      7
      x
      +
      3
      		)
      >
      (
      −
      3
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {1,2,3,4,5,...}
  • (ii)
    {0,-1,-2,-3,-4,...}
Question 11
11.
    • The simplified form of the inequality
    • (
      7
      x
      −
      3
      		)
      >
      (
      −
      9
      x
      −
      5
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    >
    (
    −
    3
    16
    		)
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    (
    −
    1
    8
    		)
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≤
    (
    −
    1
    16
    		)
    ,
    x
    ∈
    Z
  • (iv)
    x
    <
    (
    −
    3
    16
    		)
    ,
    x
    ∈
    Z
  • (v)
    x
    ≥
    (
    −
    1
    16
    		)
    ,
    x
    ∈
    Z
Question 12
12.
    • Which of the following inequations is the same as
    • (
      −
      9
      x
      −
      1
      		)
      <
      (
      3
      x
      +
      1
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    4
    x
    −
    5
    		)
    <
    (
    3
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    4
    x
    −
    5
    		)
    >
    (
    3
    x
    +
    1
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    9
    x
    −
    1
    		)
    >
    (
    8
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    9
    x
    −
    1
    		)
    <
    (
    8
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    4
    x
    −
    5
    		)
    <
    (
    8
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
Question 13
13.
    • Which of the following inequations is not the same as
    • (
      2
      x
      +
      4
      		)
      ≥
      (
      −
      2
      x
      +
      2
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    18
    x
    −
    36
    		)
    ≤
    (
    18
    x
    −
    18
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    4
    x
    +
    8
    		)
    ≥
    (
    −
    4
    x
    +
    4
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    16
    x
    −
    32
    		)
    ≤
    (
    16
    x
    −
    16
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    18
    x
    −
    36
    		)
    ≥
    (
    −
    4
    x
    +
    4
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    2
    x
    +
    4
    		)
    ≥
    (
    −
    2
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
Question 14
14.
    • Which of the following inequations is not the same as
    • (
      −
      2
      x
      +
      4
      		)
      ≤
      (
      −
      3
      x
      +
      5
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    10
    x
    +
    3
    		)
    ≤
    (
    −
    11
    x
    +
    4
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    2
    x
    −
    1
    		)
    ≤
    x
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    10
    x
    +
    3
    		)
    ≤
    (
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    5
    x
    +
    5
    		)
    ≤
    (
    4
    x
    +
    6
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    2
    x
    +
    1
    		)
    ≤
    (
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
Question 15
15.
    • The solution set of the inequality
    • (
      x
      +
      3
      		)
      ≤
      5
      ,
      x
      ∈
      Z
    • is
  • (i)
    {3,4,5,6,7,...}
  • (ii)
    {-1,-2,-3,-4,-5,...}
  • (iii)
    {2,1,0,-1,-2,...}
  • (iv)
    {2,3,4,5,6,...}
  • (v)
    {-1,0,1,2,3,...}
Question 16
16.
    • Identify the solution for the inequality
    • (
      −
      6
      x
      +
      48
      		)
      ≥
      0
      ,
      x
      ∈
      Z
  • (i)
    III
  • (ii)
    I
  • (iii)
    II
  • (iv)
    IV
Question 17
17.
    • Which of the following inequations is not the same as
    • (
      −
      7
      x
      +
      3
      		)
      <
      (
      7
      x
      +
      7
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    5
    x
    +
    10
    		)
    <
    (
    9
    x
    +
    14
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    11
    x
    −
    2
    		)
    <
    (
    3
    x
    +
    2
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    9
    x
    +
    6
    		)
    <
    (
    5
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    5
    x
    +
    3
    		)
    <
    (
    9
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    9
    x
    +
    6
    		)
    <
    (
    9
    x
    +
    7
    		)
    ,
    x
    ∈
    Z
Question 18
18.
    • Which of the following figures represents the solution set
    • {7,6,5,4,3,2,...}
  • (i)
    I
  • (ii)
    II
  • (iii)
    III
  • (iv)
    IV
Question 19
19.
    • Solve the inequation
    • (
      −
      8
      x
      +
      48
      		)
      ≤
      0
      ,
      x
      ∈
      Z
  • (i)
    {7,8,9,10,11,...}
  • (ii)
    {6,5,4,3,2,...}
  • (iii)
    {5,4,3,2,1,...}
  • (iv)
    {6,7,8,9,10,...}
Question 20
20.
Which of the following is not an inequation?
  • (i)
    (
    −
    2
    x
    −
    1
    		)
    =
    (
    −
    7
    x
    +
    5
    		)
  • (ii)
    (
    9
    x
    −
    5
    		)
    ≤
    (
    −
    8
    x
    −
    1
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    −
    8
    x
    −
    4
    		)
    >
    (
    −
    9
    x
    +
    5
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    6
    x
    −
    4
    		)
    <
    (
    −
    4
    x
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    −
    7
    x
    +
    9
    		)
    ≥
    (
    −
    9
    x
    −
    1
    		)
    ,
    x
    ∈
    Z
Question 21
21.
    • Which of the following inequations is not the same as
    • (
      −
      5
      x
      		)
      ≥
      (
      9
      x
      −
      3
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    −
    13
    x
    		)
    ≥
    (
    x
    −
    3
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    −
    7
    x
    +
    9
    		)
    ≥
    (
    16
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    2
    x
    −
    7
    		)
    ≥
    (
    16
    x
    −
    10
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    −
    7
    x
    +
    9
    		)
    ≥
    (
    7
    x
    +
    6
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    2
    x
    −
    6
    		)
    ≥
    (
    16
    x
    −
    9
    		)
    ,
    x
    ∈
    Z
Question 22
22.
    • The solution set of the inequality
    • (
      2
      x
      −
      4
      		)
      <
      (
      −
      7
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    {-2,-3,-4,-5,-6,...}
  • (ii)
    {2,1,0,-1,-2,...}
  • (iii)
    {0,1,2,3,4,...}
  • (iv)
    {-1,0,1,2,3,...}
Question 23
23.
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 positive number on both sides does not change the inequality
d)
Dividing same negative number on both sides does not change the inequality
e)
Adding same number on both sides does not change the inequality
f)
Subtracting same number on both sides does not change the inequality
  • (i)
    {a,c,e,f}
  • (ii)
    {b,f,a}
  • (iii)
    {d,c}
  • (iv)
    {b,d,e}
  • (v)
    {b,a}
Question 24
24.
    • Which of the following inequations is the same as
    • (
      8
      x
      +
      1
      		)
      ≥
      (
      x
      +
      8
      		)
      ,
      x
      ∈
      Z
  • (i)
    (
    5
    x
    +
    3
    		)
    <
    (
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (ii)
    (
    5
    x
    +
    3
    		)
    >
    (
    x
    +
    8
    		)
    ,
    x
    ∈
    Z
  • (iii)
    (
    8
    x
    +
    1
    		)
    >
    (
    −
    2
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
  • (iv)
    (
    8
    x
    +
    1
    		)
    <
    (
    −
    2
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
  • (v)
    (
    5
    x
    +
    3
    		)
    ≥
    (
    −
    2
    x
    +
    10
    		)
    ,
    x
    ∈
    Z
Question 25
25.
    • The simplified form of the inequality
    • (
      −
      3
      x
      +
      6
      		)
      ≥
      (
      6
      x
      −
      7
      		)
      ,
      x
      ∈
      Z
    • is
  • (i)
    x
    <
    14
    9
    ,
    x
    ∈
    Z
  • (ii)
    x
    >
    14
    9
    ,
    x
    ∈
    Z
  • (iii)
    x
    ≥
    4
    3
    ,
    x
    ∈
    Z
  • (iv)
    x
    ≤
    4
    3
    ,
    x
    ∈
    Z
  • (v)
    x
    ≤
    13
    9
    ,
    x
    ∈
    Z
    Assignment Key
  •  1) (i)
  •  2) (i)
  •  3) (ii)
  •  4) (ii)
  •  5) (ii)
  •  6) (iii)
  •  7) (i)
  •  8) (iv)
  •  9) (v)
  •  10) (ii)
  •  11) (ii)
  •  12) (v)
  •  13) (iv)
  •  14) (iii)
  •  15) (iii)
  •  16) (ii)
  •  17) (v)
  •  18) (iv)
  •  19) (iv)
  •  20) (i)
  •  21) (ii)
  •  22) (i)
  •  23) (i)
  •  24) (v)
  •  25) (v)