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20 Jun 2015, 12:14
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What is the value of \(x\)?
(1) \((|x| + 9)(x - 9) = 0\)
(2) \((|x| - 9)(x + 9) = 0\)
(1) \((|x| + 9)(x - 9) = 0\)
(2) \((|x| - 9)(x + 9) = 0\)
20 Jun 2015, 12:14
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Official Solution:
What is the value of \(x\)?
(1) \((|x| + 9)(x - 9) = 0\)
For the product of two factors to equal 0, at least one of them must be 0. Since \(|x| + 9\) is the sum of a nonnegative and a positive value, it will always be positive and cannot be 0. Therefore, \(x - 9 = 0\), which implies \(x = 9\). Sufficient.
(2) \((|x| - 9)(x + 9) = 0\)
Either \(|x| - 9 = 0\) or \(x + 9 = 0\). This means \(x\) can be either 9 or -9. Not sufficient.
Answer: A
What is the value of \(x\)?
(1) \((|x| + 9)(x - 9) = 0\)
For the product of two factors to equal 0, at least one of them must be 0. Since \(|x| + 9\) is the sum of a nonnegative and a positive value, it will always be positive and cannot be 0. Therefore, \(x - 9 = 0\), which implies \(x = 9\). Sufficient.
(2) \((|x| - 9)(x + 9) = 0\)
Either \(|x| - 9 = 0\) or \(x + 9 = 0\). This means \(x\) can be either 9 or -9. Not sufficient.
Answer: A
06 May 2023, 02:42
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
