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Intern Joined: 07 Oct 2017
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|3x+7| >= 2x+12 which of the following is x value: [#permalink] 00:00

Question Stats: 75% (00:42) correct 25% (00:01) wrong based on 8 sessions
$$|3x+7| \geq{2x+12}$$ 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.
Moderator  Joined: 18 Apr 2015
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Re: Absolute Inequality [#permalink]
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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Intern Joined: 07 Oct 2017
Posts: 8
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Kudos [?]: 3 , given: 0

Re: Absolute Inequality [#permalink]
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.
Moderator  Joined: 18 Apr 2015
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Re: Absolute Inequality [#permalink]
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.
_________________ Senior Manager Joined: 20 May 2014
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]
1
KUDOS
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"?
Director Joined: 20 Apr 2016
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]
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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Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html Re: |3x+7| >= 2x+12 which of the following is x value:   [#permalink] 09 Oct 2017, 04:46
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