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concept Q regarding Absolute values

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concept Q regarding Absolute values [#permalink] New post 21 Sep 2010, 07:01
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] New post 21 Sep 2010, 08:03
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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Director
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Re: concept Q regarding Absolute values [#permalink] New post 21 Sep 2010, 12:53
thanks for the clarification
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Re: concept Q regarding Absolute values   [#permalink] 21 Sep 2010, 12:53
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