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# |3x+7| >= 2x+12 which of the following is x value:

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|3x+7| >= 2x+12 which of the following is x value: [#permalink]  07 Oct 2017, 14:14
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|3x+7| \geq{2x+12} which of the following is x value:

(A) x\leq{-\frac{19}{5}}

(B) x\geq{-\frac{19}{5}}

(C) x\leq{5}

(D) x\leq{-\frac{19}{5}} or x\geq{5}

(E) \frac{-19}{5} < x < 5
[Reveal] Spoiler: OA

Last edited by f4h6 on 09 Oct 2017, 06:29, edited 4 times in total.
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Re: Absolute Inequality [#permalink]  08 Oct 2017, 03:07
Expert's post
Please, could you post the entire question here on the board as it is from MGRE ?? So we can help you more.

Thank you so much
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Re: Absolute Inequality [#permalink]  08 Oct 2017, 06:47
Carcass wrote:
Please, could you post the entire question here on the board as it is from MGRE ?? So we can help you more.

Thank you so much

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Re: Absolute Inequality [#permalink]  08 Oct 2017, 09:24
Expert's post
I do not know why is D the answer unless the X takes negative values.

For positive values the answer is E.

Waiting expert.
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]  08 Oct 2017, 22:23
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f4h6 wrote:
|3x+7| \geq{2x+12} which of the following is x value:

(A) x\leq{-\frac{19}{5}}

(B) x\geq{-\frac{19}{5}}

(C) x\leq{5}

(D) x\leq{-\frac{19}{5}} or x\geq{5}

(E) \frac{-19}{5} < x < 5

After solving the inequality I got the two answers X >=5 and X <= -19/5. but since this is an absolute question I checked each answer by plug in the two possible answers in the original equation and I found that x <= -19/5 is an erroneous value, so I chose answer choice (C) as the correct answer, but the book gives (D) as the correct answer. what I'm missing here

|3x+7| \geq{2x+12} is true when x \geq 5 or x \leq \frac{19}{5}. Which is option D.

P.S. Does the question is worded exactly as you written? Does it say "which of the following is x value"?
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]  09 Oct 2017, 04:46
f4h6 wrote:
|3x+7| \geq{2x+12} which of the following is x value:

Here we have to consider both positive and negative values of (3x +7) since it under |3x+7|

Considering +ve we get -

3x+7 \geq{2x+12}

or 3x \geq 2x + 5

or x \geq 5

Now considering negative

-(3x+7) \geq{2x+12}

or 3x +7 \leq -(2x+12)

or 3x +7 \leq -2x-12

or 5x \leq -19

or x \leq -19/5.

Therefore x \geq 5 or x \leq -19/5

Hence option D
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Re: |3x+7| >= 2x+12 which of the following is x value:   [#permalink] 09 Oct 2017, 04:46
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