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# If |3a + 7| ≥ 2a + 12, then

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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 ≥ 5And 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