[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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How many values of x satisfy the equation ||x-7|-9|=11?
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Max@Math Revolution
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Case 1: |x-7| - 9 = 11Max@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
|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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Max@Math Revolution
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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
||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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