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01 Mar 2022, 03:00
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D
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If \(2p ≥ q − 1\) and \(p + 4 ≥ 3q\), which of the following must be true?
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
01 Mar 2022, 08:47
Kudos
Bookmarks
Bunuel
If \(2p ≥ q − 1\) and \(p + 4 ≥ 3q\), which of the following must be true?
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
Key property: If the inequality symbols of two inequalities are facing the same direction, we can add those inequalities.
That's the case with our given inequalities:
\(2p ≥ q − 1\)
\(p + 4 ≥ 3q\)
Add the inequalities to get: \((2p) + (p + 4) ≥ (q − 1) + (3q)\)
Simplify to get: \(3p+4 ≥ 4q-1\)
Answer: D
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01 Mar 2022, 09:00
Kudos
Bookmarks
Bunuel
If \(2p ≥ q − 1\) and \(p + 4 ≥ 3q\), which of the following must be true?
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
\(2p ≥ q − 1\) and \(p + 4 ≥ 3q\)(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
Or, \(3p + 4 ≥ 4q - 1\), Answer will be (D)
