document.write( "Question 984772: x/|x| < x
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Algebra.Com's Answer #605597 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "1. The domain of the function $\"x%2Fabs%28x%29\"$ is the set of all real numbers except of x=0. \r
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\n" ); document.write( "\n" ); document.write( "2. If x > 0, then $\"x%2Fabs%28x%29\"$ = $\"x%2Fx\"$ = 1, and the given inequality takes the form   1 < x,   i.e. x > 1.\r
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\n" ); document.write( "\n" ); document.write( "3. If x < 0, then $\"x%2Fabs%28x%29\"$ = $\"x%2F%28-x%29\"$ = -1, and the given inequality takes the form   -1 < x,   i.e. x > -1.\r
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\n" ); document.write( "\n" ); document.write( "Answer. The solution of the given inequality is the union of two sets of real numbers:   1) x > 1   and   2) -1 < x < 0.\r
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