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If −x − 2 = −|−(6 − 2)|, then x =

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If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 15 Jun 2017, 07:33
1
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A
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D
E

Difficulty:

  5% (low)

Question Stats:

90% (00:48) correct 10% (00:59) wrong based on 318 sessions

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If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 15 Jun 2017, 07:42
Bunuel wrote:
If \(−x − 2 = −|−(6 − 2)|\), then x =

(A) –5
(B) –2
(C) 0
(D) 2
(E) 5


\(−x − 2 = −|−(6 − 2)|\)
\(-x - 2 = −|−4|\)
\(-(4) = -x -2\)
\(x = 4-2 = 2\) . Answer D...
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 15 Jun 2017, 08:29
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Top Contributor
Bunuel wrote:
If \(−x − 2 = −|−(6 − 2)|\), then x =

(A) –5
(B) –2
(C) 0
(D) 2
(E) 5


Given: −x − 2 = −|−(6 − 2)|
Simplify right side: −x − 2 = −|−(4)|
Evaluate right side: −x − 2 = −(4)
Simplify right side: −x − 2 = −4
Add 2 to both sides: −x = -2
Multiply both sides by -1 to get: x = 2

Answer:

Cheers,
Brent
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If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 15 Jun 2017, 09:09
GMATPrepNow wrote:
Bunuel wrote:
If \(−x − 2 = −|−(6 − 2)|\), then x =

(A) –5
(B) –2
(C) 0
(D) 2
(E) 5


Given: −x − 2 = −|−(6 − 2)|
Simplify right side: −x − 2 = −|−(4)|
Evaluate right side: −x − 2 = −(4)
Simplify right side: −x − 2 = −4
Add 2 to both sides: −x = -2
Multiply both sides by -1 to get: x = 2

Answer:

Cheers,
Brent

GMATPrepNow , Brent, I have a feeling this is a really dumb question, but I am confused.

I considered two cases, the one you showed, and
-|-(4)| = - (-x - 2)
-(4) = x + 2
- 6 = x

Upon plugging in (x = -6) into original equation, it did not satisfy (LHS became +4, not negative value as needed). So I plugged in x = 2, and it worked.

Question: when do you know that you do not need to consider both cases? I thought about whether or not I'd be able to "see," immediately, that the alternative case would not yield a negative LHS. Not likely.

Maybe this kind of equation never requires more than one case? What am I missing?
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 15 Jun 2017, 12:24
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Top Contributor
1
genxer123 wrote:
Brent, I have a feeling this is a really dumb question, but I am confused.

I considered two cases, the one you showed, and
-|-(4)| = - (-x - 2)
-(4) = x + 2
- 6 = x

Upon plugging in (x = -6) into original equation, it did not satisfy (LHS became +4, not negative value as needed). So I plugged in x = 2, and it worked.

Question: when do you know that you do not need to consider both cases? I thought about whether or not I'd be able to "see," immediately, that the alternative case would not yield a negative LHS. Not likely.

Maybe this kind of equation never requires more than one case? What am I missing?


We need to consider two cases when there are variables inside the absolute value symbols.
For example, if we have |x - 2| = 6, then we must consider two cases:
case a: x - 2 = 6
case b: x - 2 = -6

If there are no variables inside the absolute value symbols, then we need not consider two cases.
For example, in the equation x = |3|, we can conclude that x = 3

Conversely, in the equation |x| = 3, we can conclude that x = 3 or x = -3

Cheers,
Brent
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 19 Jun 2017, 11:36
This is an amazing question. Adding to my list of must do questions to re-do.
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 24 Jun 2017, 15:40
\(−x − 2 = −|−(6 − 2)|\)

\(-x - 2 = -|-(4)|\)

\(-x - 2 = -| 4 |\)

\(-x - 2 = -4\)

\(- x = - 2\)

\(x = 2\)

Hence, Answer is D
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 06 Jul 2017, 17:28
Bunuel wrote:
If \(−x − 2 = −|−(6 − 2)|\), then x =

(A) –5
(B) –2
(C) 0
(D) 2
(E) 5


We can simplify the equation:

-x - 2 = -|-(6 - 2)|

-x - 2 = -|-(4)|

-x - 2 = -4

-x = -2

x = 2

Answer: D
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Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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New post 13 Jul 2017, 08:48
Correct option:D
Time take: 0:56 sec
Solution
-x-2=-|-(6-2)|
-x-2=-|-4|
-x-2=-4
-x=-2
Dividing both sides by minus
x=2
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Re: If −x − 2 = −|−(6 − 2)|, then x =   [#permalink] 13 Jul 2017, 08:48
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If −x − 2 = −|−(6 − 2)|, then x =

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