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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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60% (00:38) correct 40% (00:01) wrong based on 5 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.
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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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