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# concept Q regarding Absolute values

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concept Q regarding Absolute values [#permalink]  21 Sep 2010, 06:01
Hi i had a concept Q regarding Absolute values with inequalities

For the below Eq

|x + 4 | <= 3

Case 1 : x + 4 <= 3 or x <= -1

Case 2 :

x + 4 <= -3 or is it
x + 4 >= -3

do we flip the sign for case 2 ?
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Re: concept Q regarding Absolute values [#permalink]  21 Sep 2010, 07:03
Expert's post
rxs0005 wrote:
Hi i had a concept Q regarding Absolute values with inequalities

For the below Eq

|x + 4 | <= 3

Case 1 : x + 4 <= 3 or x <= -1

Case 2 :

x + 4 <= -3 or is it
x + 4 >= -3

do we flip the sign for case 2 ?

For second case it's $$-(x+4)\leq{3}$$ --> $$x+4\geq{-3}$$

Correct approach for expanding $$|x+4|\leq{3}$$, would be:
$$x<-4$$ --> $$|x+4|=-x-4$$ --> $$-x-4\leq{3}$$ --> $$x\geq{-7}$$ --> $${-7}\leq{x}<-4$$;
$$x\geq{-4}$$ --> $$|x+4|=x+4$$ --> $$x+4\leq{3}$$ --> $$x\leq{-1}$$ --> $$-4\leq{x}\leq{-1}$$;

Final range: $$-7\leq{x}\leq{-1}$$.
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Re: concept Q regarding Absolute values [#permalink]  21 Sep 2010, 11:53
thanks for the clarification
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Re: concept Q regarding Absolute values   [#permalink] 21 Sep 2010, 11:53
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