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If |3a + 7| 2a + 12, then [#permalink]
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Given that \(|3a + 7| ≥ 2a + 12\) and we need to find the range for a

\(|3a + 7| ≥ 2a + 12\)



We will have two cases
-Case 1: 3a + 7 ≥ 0

=> 3a ≥ -7
=> a ≥ \(\frac{-7}{3}\)
=> |3a + 7| = 3a + 7
=> 3a + 7 ≥ 2a + 12
=> a ≥ 5

And our condition was a ≥ \(\frac{-7}{3}\)
=> a ≥ 5 is a SOLUTION
-Case 2: 3a + 7 < 0

=> 3a < -7
=> a < \(\frac{-7}{3}\) ~ -2.3
=> |3a + 7| = -(3a + 7)
=> -3a - 7 ≥ 2a + 12 => 5a ≤ -19
=> a ≤ \(\frac{-19}{5}\) (=-3.8)

And our condition was a < \(\frac{-7}{3}\)
=> a ≤ \(\frac{-19}{5}\) is a SOLUTION


So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

GMAT Club Bot
If |3a + 7| 2a + 12, then [#permalink]
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