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# If −x − 2 = −|−(6 − 2)|, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 54496
If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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15 Jun 2017, 07:33
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If $$−x − 2 = −|−(6 − 2)|$$, then x =

(A) –5
(B) –2
(C) 0
(D) 2
(E) 5

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Joined: 04 Dec 2015
Posts: 750
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If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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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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Joined: 12 Sep 2015
Posts: 3589
Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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15 Jun 2017, 08:29
1
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

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

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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

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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Joined: 12 Sep 2015
Posts: 3589
Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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15 Jun 2017, 12:24
1
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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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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24 Jun 2017, 15:40
$$−x − 2 = −|−(6 − 2)|$$

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

$$-x - 2 = -| 4 |$$

$$-x - 2 = -4$$

$$- x = - 2$$

$$x = 2$$

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

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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

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Joined: 06 Feb 2017
Posts: 7
Re: If −x − 2 = −|−(6 − 2)|, then x =  [#permalink]

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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
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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