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# If |y|≤ - 4x and |3x - 4|= 2x + 6

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Joined: 22 Aug 2018
Posts: 26
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Kudos [?]: 4 [0], given: 4

If |y|≤ - 4x and |3x - 4|= 2x + 6 [#permalink]  22 Aug 2018, 06:42
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Question Stats:

40% (01:28) correct 60% (01:20) wrong based on 5 sessions
The question in 5lb. Manhattan,

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) $$10$$

How to solve such a question? I get a lot of confused while solving inequality question. It would be appreciable if someone could share tips or tricks, or any kind of pdf.
[Reveal] Spoiler: OA
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Joined: 18 Apr 2015
Posts: 5917
Followers: 96

Kudos [?]: 1158 [1] , given: 5488

Re: Two unkowns in inequalities [#permalink]  22 Aug 2018, 07:48
1
KUDOS
Expert's post
Hi,

please before to post a question look at the rules of the board for posting https://greprepclub.com/forum/rules-for ... -1083.html

Post it under the right sub-forum NOT in general quant section that is reserved for strategies and else.

Also, read how to format a question in a proper manner https://greprepclub.com/forum/qq-how-to ... -2357.html

Back to the question:

Since |y|≤ - 4x, we have x≤ 0 (Absolute value is non-negative)
Given, |3x - 4|= 2x + 6 when 3x-4>0 or x>$$\frac{4}{3}$$ (Not possible since x is not positive)

Again |3x - 4|=-(3x-4)=2x + 6
Or, 4-3x=2x+6
Or, 5x=-2
Or, $$x=\frac{-2}{5}$$

Hope this helps
_________________
Re: Two unkowns in inequalities   [#permalink] 22 Aug 2018, 07:48
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