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ICSE-VIII-Mathematics

15: Linear Inequations Class 8 Maths

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    Section : A
  • Qstn #1
    If the replacement set is the set of natural numbers, solve.
  • #1-i
    x - 5 < 0
    Ans : x - 5 < 0
    ⇒ x - 5 + 5 < 0 + 5 ...(Adding 5)
    ⇒ x < 5
    Required answer = {1, 2, 3, 4}
  • #1-ii
    x + 1 < 7
    Ans : x + 1 ≤ 7⇒ x + 1 - 1 ≤ 7 - 1 (Subtracting 1)
    ⇒ x ≤ 6
    Required answer = {1, 2, 3, 4, 5, 6}
  • #1-iii
    3x - 4 > 6
    Ans : 3x - 4 > 6
    3x - 4 + 4 > 6 + 4 (Adding 4)
    ⇒ 3x > 10
    ⇒ 3x/3 > 10/3 ...(Dividing by 3)
    ⇒ x > 10/3
    ⇒ x > 3 1/3
    Required answer = {4, 5, 6, ...}
  • #1-iv
    4x + 1 > 17
    Ans : 4x + 1 ≥ 17
    ⇒ 4x + 1 - 1 ≥ 17 - 1 (Subtracting)
    ⇒ 4x ≥ 16
    ⇒ 4x/4 ≥ 16/4 (Dividing by 4)
    ⇒ x ≥ 4
    Required answer = {4, 5, 6, ...}
  • Qstn #2
    If the replacement set = {-6, -3, 0, 3, 6, 9}; find the truth set of the following:
  • #2-i
    2x - 1 > 9
    Ans : 2x - 1 > 9
    ⇒ 2x - 1 + 1 > 9 + 1 (Adding 1)
    ⇒ 2x > 10
    ⇒ x > 5 (Dividing by 2)
    ⇒ x > 5
    Required answer = {6, 9}
  • #2-ii
    3x + 7 < 1
    Ans : 3x + 7 ≤ 1
    ⇒ 3x + 7 - 7 ≤ 1 - 7 (Subtracting 7)
    ⇒ 3x ≤ - 6
    ⇒ x ≤ - 2
    Required Answer = {-6, -3}
  • Qstn #3
    Solve 7 > 3x - 8; x ∈ N
    Ans : 7 > 3x - 8
    ⇒ 7 - 3x > 3x - 3x - 8 (Subtracting 3x)
    ⇒ 7 - 7 - 3x > 3x - 3x - 8 - 7 (Subtracting 7)
    ⇒ -3x > -15
    ⇒ x < 5 (Dividing by -3)
    Required Answer = {1, 2, 3, 4}
    Note : Division by negative number reverses the inequality.
  • Qstn #4
    -17 < 9y - 8 ; y ∈ Z
    Ans : -17 < 9y - 8
    ⇒ -17 + 8 < 9y - 8 + 8 (Adding 8)
    ⇒ -9 < 9y
    ⇒ -1 < y (Dividing by 9)
    Required number = {0, 1, 2, 3, 4, ...}
  • Qstn #5
    Solve 9x - 7 ≤ 28 + 4x; x ∈ W
    Ans : 9x - 1 ≤ 28 + 4x
    ⇒ 9x - 4x - 7 ≤ 28 + 4x - 4x (Subtracting 4x)
    ⇒ 5x - 7 ≤ 28
    ⇒ 5x - 7 + 7 ≤ 28 + 7 (Adding 7)
    ⇒ 5x ≤ 35
    ⇒ x ≤ 7 (Dividing by 5)
    Required answer = {0, 1, 2, 3, 4, 5, 6, 7}
  • Qstn #6
    Solve : 2/3x + 8 < 12 ; x ∈ W
    Ans : 2/3x + 8 < 12
    ⇒ 2/3x + 8 - 8 < 12 - 8
    ⇒ 2/3x < 4
    ⇒ 2/3x × 3/2 < 4 × 3/2 (Multiplying by 3/2)
    ⇒ x < 6
    ∴ Required answer = {0, 1, 2, 3, 4, 5}
  • Qstn #7
    Solve : -5(x + 4) > 30 ; x ∈ Z
    Ans : -5 = (x + 4) > 30/-5 ...(Dividing by - 5)
    Note: Division by a negative number reverses the equality
    ⇒ x + 4 < -6
    ⇒ x + 4 - 4 < - 6 - 4 (Subtracting 4)
    ⇒ x < -10
    ∴ Required Answer = {-11, -12, -13, .....}
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