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If |x-2|<4 then the solution set will be

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Carcass
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If |x-2|<4 then the solution set will be [#permalink] New post   Updated on: 29 Jun 2021, 10:13
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If \(|x-2| \leq 4\) then the solution set will be

Select all that apply

A. \(2 \leq x \leq 6\)

B. \(-2 \leq x \leq 6
\)

C. \(2 \leq x \leq -6\)

D. \(-2 \leq x \leq -6\)

E. \(2 \geq - x \geq - 6\)


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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B,E

Originally posted by Carcass on 19 Apr 2021, 12:48.
Last edited by Carcass on 29 Jun 2021, 10:13, edited 1 time in total.
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   20 Apr 2021, 22:55
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Carcass wrote:
If \(|x-2| \leq 4\) then the solution set will be

Select all that apply

A. \(2 \leq x \leq 6\)

B. \(-2 \leq x \leq 6
\)

C. \(2 \leq x \leq -6\)

D. \(-2 \leq x \leq -6\)

E. \(2 \geq x \geq 6\)


Carcass
Can you please check the option choices again?
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   20 Apr 2021, 23:21
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They are correct
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KarunMendiratta
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   20 Apr 2021, 23:28
Carcass wrote:
They are correct


\(2 ≥ x ≥ 6\)

How come 2 is greater than x which is greater than 6?
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   21 Apr 2021, 01:19
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plz explain option e...how it is correct...
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   21 Apr 2021, 03:12
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KarunMendiratta wrote:
Carcass wrote:
They are correct


\(2 ≥ x ≥ 6\)

How come 2 is greater than x which is greater than 6?


You are right. maybe a typo

From logic it must be -6

I fixed in the answer choices. Now have to be fine

Many Thanks

Regards
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   27 Jun 2021, 23:21
how the option E is correct
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   30 Jun 2021, 04:37
For Option E, if you multiply it with the negative sign then you will get the same set as that of option B.
When you multiply the inequality with the negative sign make sure you flip the inequalities.
So it will become -2<=x<=6
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Re: If |x-2|<4 then the solution set will be [#permalink] New post   30 Jun 2021, 06:17
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taskforce wrote:
For Option E, if you multiply it with the negative sign then you will get the same set as that of option B.
When you multiply the inequality with the negative sign make sure you flip the inequalities.
So it will become -2<=x<=6


|x - 2| ≤ 4

Case I:
x - 2 ≤ 4
x ≤ 6

Case II:
-(x - 2) ≤ 4
-x + 2 ≤ 4
-x ≤ 2

Multiplying both sides by -1 [The inequality will flip];
x ≥ -2

Therefore, x must lie between -2 and 6
i.e. -2 ≤ x ≤ 6

On multiplying by -1, it will be
2 ≥ -x ≥ -6

Hence, option B and E
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Re: If |x-2|<4 then the solution set will be [#permalink]
30 Jun 2021, 06:17
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