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

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

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[GMAT math practice question]

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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Max@Math Revolution wrote:
[GMAT math practice question]

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

A. 1
B. 2
C. 3
D. 4
E. 5
Case 1: |x-7| - 9 = 11
|x-7| = 20
If x-7 = 20, then x=27.
If x-7 = -20, then x = -13.

Case 2: |x-7| - 9 = -11
|x-7| = -2
Since an absolute value cannot be equal to a negative, Case 2 is not possible.

Only the values in blue are viable solutions.

The correct answer is B.

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=>

||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

Therefore, the answer is B.

Answer: B

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

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