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# If |x+4|/2>5 and x<0, which of the following could be the va

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If |x+4|/2>5 and x<0, which of the following could be the va [#permalink]  08 Aug 2018, 16:09
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Question Stats:

62% (00:33) correct 37% (00:49) wrong based on 78 sessions
If $$\frac{|x+4|}{2}>5$$ and $$x<0$$, which of the following could be the value of x?

Indicate all such values

A. -6

B. -14

C. -18
[Reveal] Spoiler: OA

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Intern
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink]  11 Aug 2018, 12:16
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Simple case of solving an inequality, given our constraint that x < 0.

|x+4|/2 > 5

Multiply both sides by 2

|x+4| > 10

Here we have two cases:

x+4 > 10

or

x+4 < -10

In both cases we subtract both sides by 4

x > 6

or

x < -14

Only the second inequality fits the constraint that x < 0

And only C is correct if x < -14 (note that it's strictly less than -14, not less than or equal to).
Manager
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink]  05 Mar 2020, 14:25
Romang67 wrote:
Simple case of solving an inequality, given our constraint that x < 0.

|x+4|/2 > 5

Multiply both sides by 2

|x+4| > 10

Here we have two cases:

x+4 > 10

or

x+4 < -10

In both cases we subtract both sides by 4

x > 6

or

x < -14

Only the second inequality fits the constraint that x < 0

And only C is correct if x < -14 (note that it's strictly less than -14, not less than or equal to).

So when we set the 10 to negative we have to flip the inequality sign?
Founder
Joined: 18 Apr 2015
Posts: 13304
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Kudos [?]: 3366 [0], given: 12159

Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink]  05 Mar 2020, 14:44
Expert's post
In this PDF the math concepts you should know to prepare for this test

Attachment:
GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]

Regards
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Re: If |x+4|/2>5 and x<0, which of the following could be the va   [#permalink] 05 Mar 2020, 14:44
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