Match the column:
Column I | Column II |
(i) Set of all values of x satisfying the inequation is | [A] (– ∞,0) ∪ (0,2) ∪(2,∞) |
(ii) Set of all values of x satisfying the inequation |x| + |x – 3| > 3 is | [B] (–∞,–5) ∪ (–3,3) ∪(5,∞) |
(iii) Set of all values of x satisfying the inequation is | [C] (–∞,–1) ∪ (–1,0) ∪ (3,∞) |
(iv) Set of all values of x satisfying the inequation is | [D] (– ∞,0) ∪ (3, ∞) |
Text Solution
Verified by Experts(i) [C]; (ii) [D]; (iii) [B]; (iv) [A]
Ans.
(i) [C]
(ii) [D]
(iii) [B]
(iv) [A]
Sol. (i) 5x + 1 < (x + 1) 2 {x ≠ – 1}
⇒ x 2 – 3x > 0 ⇒ x(x – 3) > 0
∴ x ∈ (– ∞ , 0) ∪ (3, ∞ ) ~ {– 1}
(ii) |x| + |x – 3| > 3
case (i) x < 0 . . . (1)
– x + 3 – x > 3 ⇒ x < 0 . . . (2)
from (1) & (2) x ∈ (– ∞ , 0)
case (ii) 0 ≤ x < 3 . . . (3)
x + 3 – x > 3 ⇒ 3 > 3
∴ No solution
case (iii) x ≥ 3 . . . (4)
2x – 3 > 3 ⇒ x > 3 . . . (5)
from (4) & (5) x ∈ (3, ∞ )
∴ combing all case x ∈ (– ∞ , 0) ∪ (3, ∞ )
(iii) 
< 0 ⇒ 
> 0
⇒ |x| > 5 or |x| < 3
⇒ x > 5 or x < – 5 . . . (1)
or – 3 < x < – 3 . . . .(2)
from (1) & (2)
x ∈ (– ∞ , – 5) ∪ (– 3, 3) ∪ (5, ∞ )
(iv) 
> 0 ∴ x ≠ 0, 2
Inequality is always true ∴ x ∈ R~ {0, 2}
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