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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   45% (medium)

Question Stats: 70% (01:56) correct 30% (01:19) wrong based on 10 sessions

### HideShow timer Statistics How many values of $$x$$ satisfy the equation $$||x-7|-9|=11$$?

A. 1
B. 2
C. 3
D. 4
E. 5

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82

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Official Solution:

How many values of $$x$$ satisfy the equation $$||x-7|-9|=11$$?

A. 1
B. 2
C. 3
D. 4
E. 5

$$||x-7|-9| = 11$$

$$|x-7|-9 = ±11$$

$$|x-7| = 9 ±11$$

$$|x-7| = 20$$ or $$|x-7| = -2$$

$$|x-7| = 20$$ since $$|x-7| ≥ 0$$

$$x-7 = ±20$$

$$x = 7±20$$

$$x = 27$$ or $$x = -13$$

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Intern  B
Joined: 16 Mar 2018
Posts: 7

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Why does /x-7/=20 have to be > than or equal to zero?

/ symbol = absolute value sign.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82

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Paugustin90 wrote:
Why does /x-7/=20 have to be > than or equal to zero?

/ symbol = absolute value sign.

Absolute values are always greater than or equal to zero, since they are not negative.
_________________ M61-21   [#permalink] 05 Aug 2018, 23:00
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# M61-21

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