Match List-I with List-II
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List-I (Inequality) |
List-II (Solution Set) |
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(A) $2x-3<x+2≤3x+5,x∈R$ |
(I) $x ∈ (-1,∞)$ |
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(B) $|2x+3|<7, x∈R$ |
(II) $x ∈ (-∞, 120]$ |
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(C) $\frac{1}{2}(\frac{3}{5}x+4) ≥\frac{1}{3} (x-6),x∈R$ |
(III) $x ∈ (-5,2)$ |
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(D) $\frac{|x+1|}{x+1}> 0, x∈R-\{1\}$ |
(IV) $x∈[-\frac{3}{2},5)$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
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List-I (Inequality) |
List-II (Solution Set) |
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(A) $2x-3<x+2≤3x+5,x∈R$ |
(IV) $x∈[-\frac{3}{2},5)$ |
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(B) $|2x+3|<7, x∈R$ |
(III) $x ∈ (-5,2)$ |
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(C) $\frac{1}{2}(\frac{3}{5}x+4) ≥\frac{1}{3} (x-6),x∈R$ |
(II) $x ∈ (-∞, 120]$ |
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(D) $\frac{|x+1|}{x+1}> 0, x∈R-\{1\}$ |
(I) $x ∈ (-1,∞)$ |
Given inequalities and solution sets:
(A) 2x − 3 < x + 2 ≤ 3x + 5
Split: 2x − 3 < x + 2 → x < 5
x + 2 ≤ 3x + 5 → −2x ≤ 3 → x ≥ −3/2
Intersection: x ∈ [−3/2, 5] → (A) matches (IV)
(B) |2x + 3| < 7
−7 < 2x + 3 < 7 → −10 < 2x < 4 → −5 < x < 2
(B) matches (III)
(C) 1/2(3/5x + 4) ≥ 1/3(x − 6)
Multiply both sides by 6: 3*(3/5x + 4) ≥ 2*(x − 6) → (9/5)x + 12 ≥ 2x − 12
Bring terms together: 12 + 12 ≥ 2x − (9/5)x → 24 ≥ (10/5 − 9/5)x → 24 ≥ (1/5)x → x ≤ 120
(C) matches (II)
(D) (|x+1|)/(x+1) > 0
Expression positive if x + 1 > 0 → x ∈ (−1, ∞), excluding x = −1
(D) matches (I)