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If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x?

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Carcass
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If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x? [#permalink] New post   08 Aug 2018, 16:35
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If |y|≤−4x and |3x−4|=2x+6, what is the value of x?

A. −3

B. −13

C. −25

D. 13

E. 10
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kaziselim
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Re: If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x? [#permalink] New post   09 Aug 2018, 13:36
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Carcass wrote:
If |y|≤−4x and |3x−4|=2x+6, what is the value of x?

A. −3

B. −13

C. −25

D. 13

E. 10



First of all , thanks for this question that made me upset for a while. It's not that much easy. It must be at least mid level question.

Note:

|y| means the ultimate value is positive.

Given |y|≤−4x

So, -4x is positive. It clearly indicates that x is negative.

we have |3x-4| = 2x + 6

Case 1:

3x - 4 is positive .

3x - 4 = 2x + 6

x = 10

Case 2 :

(3x - 4) is negative.

-3x + 4 = 2x + 6

x = - 25

Thus x = - 2/5 as it meets out condition.

The best answer is C.
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Re: If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x? [#permalink] New post   13 Jul 2021, 23:32
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x? [#permalink]
13 Jul 2021, 23:32
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