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16 Sep 2014, 01:00
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What is the value of \(x\)?
(1) \(\frac{1}{x} + \frac{1}{x + 2} = 1\)
(2) \(x \lt |x|\)
(1) \(\frac{1}{x} + \frac{1}{x + 2} = 1\)
(2) \(x \lt |x|\)
16 Sep 2014, 01:00
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Official Solution:
What is the value of \(x\)?
(1) \(\frac{1}{x}+\frac{1}{x+2}=1\).
\(\frac{(x+2)+x}{x(x+2)}=1\);
\(2x+2=x^2+2x\);
\(x^2=2\).
This yields two possible values: \(x=\sqrt{2}\) or \(x=-\sqrt{2}\). Not sufficient.
(2) \(x \lt |x|\).
This inequality indicates that \(x < 0\). Not sufficient.
(1)+(2) Since from (2) we know that \(x < 0\), then from (1) the only possible value is \(x=-\sqrt{2}\). Sufficient.
Answer: C
What is the value of \(x\)?
(1) \(\frac{1}{x}+\frac{1}{x+2}=1\).
\(\frac{(x+2)+x}{x(x+2)}=1\);
\(2x+2=x^2+2x\);
\(x^2=2\).
This yields two possible values: \(x=\sqrt{2}\) or \(x=-\sqrt{2}\). Not sufficient.
(2) \(x \lt |x|\).
This inequality indicates that \(x < 0\). Not sufficient.
(1)+(2) Since from (2) we know that \(x < 0\), then from (1) the only possible value is \(x=-\sqrt{2}\). Sufficient.
Answer: C
04 Mar 2018, 05:55
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Hello Guys
How do we solve x<|x| ? How does it leads to x<0 ?
How do we solve x<|x| ? How does it leads to x<0 ?
