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23 Jun 2021, 08:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:36) correct
23%
(01:48)
wrong
based on 506
sessions
History
Date
Time
Result
Not Attempted Yet
If \(|3a + 7| ≥ 2a + 12\), then
(A) \(a ≤ -\frac{19}{5}\)
(B) \(a ≥ -\frac{19}{5}\)
(C) \(a ≥ 5\)
(D) \(a ≤ -\frac{19}{5}\) or \(a ≥ 5\)
(E) \(-\frac{19}{5} ≤ a ≤ 5\)
(A) \(a ≤ -\frac{19}{5}\)
(B) \(a ≥ -\frac{19}{5}\)
(C) \(a ≥ 5\)
(D) \(a ≤ -\frac{19}{5}\) or \(a ≥ 5\)
(E) \(-\frac{19}{5} ≤ a ≤ 5\)
23 Jun 2021, 08:33
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Bunuel
Case-1: If a > 0
\(|3a + 7| ≥ 2a + 12\)
i.e. \(3a + 7 ≥ 2a + 12\)
i.e. \(3a -2a ≥ 12-7\)
i.e. \(a ≥ 5\)
Case-2: If -7/3 < a < 0
let, a = -x where x >0
\(|3a + 7| ≥ 2a + 12\)
i.e. \(-3x + 7 ≥ -2x + 12\)
i.e. \(x ≤ -5\)
i.e. \(a ≥ 5\)
NOT POSSIBLE i.e. Case-2 REJECTED
Case-3: If -7/3 > a
let, a = -x where x >0
\(|3a + 7| ≥ 2a + 12\)
i.e. \(3x - 7 ≥ -2x + 12\)
i.e. \(x ≥ 19/5\)
i.e. \(a ≤ -19/5\)
i.e. \(a ≤ -\frac{19}{5}\) or \(a ≥ 5\)
ANswer: Option D
23 Jun 2021, 08:44
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Asked: If \(|3a + 7| ≥ 2a + 12\), then
\(|3a + 7| ≥ 2a + 12\)
Case 1: a >= - 7/3
3a + 7 >= 2a + 12
a >=5
a>=5 > - 7/3
Case 2: a< -7/3
-3a - 7 >= 2a + 12
5a <= -19
a <= - 19/5 < - 7/3
IMO D
\(|3a + 7| ≥ 2a + 12\)
Case 1: a >= - 7/3
3a + 7 >= 2a + 12
a >=5
a>=5 > - 7/3
Case 2: a< -7/3
-3a - 7 >= 2a + 12
5a <= -19
a <= - 19/5 < - 7/3
IMO D
