Qstnid -A-1- If The Replacement Set Is The Set Of Natural Numbers, Solve. (I) X - 5 &Lt; 0 (Ii) X + 1 &Lt; 7 (Iii) 3x - 4 &Gt; 6 (Iv) 4x + 1 &Gt; 17 - 15: Linear Inequations Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

15: Linear Inequations Class 8 Maths

with Solutions -

Qstn# A-1 Prvs-Qstn Next-Qstn

#1
If the replacement set is the set of natural numbers, solve. (i) x - 5 < 0 (ii) x + 1 < 7 (iii) 3x - 4 > 6 (iv) 4x + 1 > 17
Ans : (i) x - 5 < 0
⇒ x - 5 + 5 < 0 + 5 ...(Adding 5)
⇒ x < 5
Required answer = {1, 2, 3, 4} (ii) x + 1 ≤ 7⇒ x + 1 - 1 ≤ 7 - 1 (Subtracting 1)
⇒ x ≤ 6
Required answer = {1, 2, 3, 4, 5, 6} (iii) 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, ...} (iv) 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, ...}

#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, ...}