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

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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. \(\frac{-1}{3}\)

C. \(\frac{-2}{5}\)

D. \(\frac{1}{3}\)

E. \(10\)
[Reveal] Spoiler: OA

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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
Carcass wrote:
If \(|y| ≤ - 4x\) and |\(3x - 4| = 2x + 6\), what is the value of x?

A. \(-3\)

B. \(\frac{-1}{3}\)

C. \(\frac{-2}{5}\)

D. \(\frac{1}{3}\)

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 \(|y| \leq-4x\)

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 = - \(\frac{2}{5}\)

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

The best answer is C.
Re: If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x?   [#permalink] 09 Aug 2018, 13:36
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If |y| ≤ –4x and |3x – 4| = 2x + 6, what is the value of x?

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