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

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f4h6
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|3x+7| >= 2x+12 which of the following is x value: [#permalink] New post   Updated on: 09 Oct 2017, 06:29
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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) \(\frac{-19}{5} < x < 5\)
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D

Originally posted by f4h6 on 07 Oct 2017, 14:14.
Last edited by f4h6 on 09 Oct 2017, 06:29, edited 4 times in total.
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D
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Re: Absolute Inequality [#permalink] New post   08 Oct 2017, 03:07
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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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f4h6
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Re: Absolute Inequality [#permalink] New post   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


Thank you for your reply. I have updated the question.
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Re: Absolute Inequality [#permalink] New post   08 Oct 2017, 09:24
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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] New post   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] New post   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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