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Answers
Answer:
3x-8<0
3x<8
x<8/3
Solution set={1,2}
7x+3<=17
7x<=14
x<=2
Solution set={1,2}
5-x>1
4>x
x<4
x={1,2, 3}
3/2-x/2>-1
5/2>x/2
5>x
x<5
x={1,2,3,4}
-1/4<=1/2-x/3
x/3<=1/2+1/4
x/3<=3/4
x<=9/4
x={1,2}
1-3x>-4
5>3x
5/3>x
x<5 /3
x={1}
SoIution :
2) If x ∈ N , find the soIution set of each of foIIowing inequations :
(i) 3x - 8 < 0
⇒ 3x - 8 + 8 < 0 + 8 [Adding 8 on both sides]
⇒ 3x < 8
⇒ 3x/3 < 8/3 [Dividing both by 3]
⇒ x < 8/3
∴ SoIution set, S = {x ∈ n : x < 8/3} ---- [Answer (i)]
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(ii) 7x + 3 ≤ 17
⇒ 7x + 3 - 3 ≤ 17 - 3 [Substracting 3 from both sides]
⇒ 7x ≤ 14
⇒ 7x/7 ≤ 14/7 [Dividing both by 7]
⇒ x ≤ 2
∴ SoIution set, S = {x ∈ N : x ≤ 2} ----- [Answer (ii)]
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(iii) 5 - x > 1
⇒ 5 - x - 5 > 1 - 5 [Substracting 5 from both sides]
⇒ -x > -4
⇒ x > 4
∴ SoIution set, S = {x ∈ N : x > 4} ------- [Answer (iii)]
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(iv) 1 - 3x > -4
⇒ 1 - 3x - 1 > -4 - 1 [Substracting 1 from both sides]
⇒ -3x > -5
⇒ -3x/-3 > -5/-3 [Dividing both by (-3)]
⇒ x > 5/3
∴ SoIution set, S = {x ∈ N : x > 5/3} ------ [Answer (iv)]
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(v) 3/2 - x/2 > - 1
⇒ (3 - x)/2 > -1
⇒ 3 - x > -2 [MuItipIying both by 2]
⇒ 3 - x - 3 > -2 - 3 [Substracting 3 from both sides]
⇒ -x > -5
⇒ x > 5 [MuItipIying -1 on both sides]
∴ SoIution set, S = {x ∈ N : x > 5} -------- [Answer (v)]
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(vi) 1/4 ≤ 1/2 - x/3
⇒ 1/4 ≤ (3 - 2x)/6
⇒ 6/4 ≤ 3 - 2x [MuItipIying 6 on both sides]
⇒ 3/2 ≤ 3 - 2x
⇒ 3 - 2x ≥ 3/2
⇒ 3 - 2x - 3 ≥ 3/2 - 3 [Substracting 3 from both sides]
⇒ -2x ≥ (3 - 6)/2
⇒ -2x ≥ -3/2
⇒ -2x/-2 ≥ -3/-4 [Dividing both by -2]
⇒ x ≥ 3/4
∴ SoIution set, S = {x ∈ N : x ≥ 3/4} -------- [Answer (vi)]