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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] New post   08 Aug 2018, 16:09
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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
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C
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Romang67
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink] New post   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).
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink] New post   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?
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink] New post   05 Mar 2020, 14:44
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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]
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink] New post   16 May 2021, 08:34
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Solution:

In order to solve this one, we only need to know the basic concepts and division.

\(\frac{|x+4|}{2}\)>5
This means that, |x+4|>10
As x<0, x<-14 (|-14+4|=10)

Thus, any values below -14 will satisfy.

IMO C

Hope this helps!
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Re: If |x+4|/2>5 and x<0, which of the following could be the va [#permalink]
16 May 2021, 08:34
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