document.write( "Question 860535: The solution of the inequality: -x < x^2 < 2x + 1, is { ?? < x < ??}\r
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Algebra.Com's Answer #518483 by josgarithmetic(39620) $\"\"$ $\"About$

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Analyze two separate inequalities.\r
\n" ); document.write( "\n" ); document.write( " $\"-x%3Cx%5E2\"$ AND $\"x%5E2%3C2x%2B1\"$ ; look for what is true for both at the same time.\r
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\n" ); document.write( "\n" ); document.write( " $\"-x%5E2-x%3C0\"$
\n" ); document.write( " $\"x%5E2%2Bx%3E0\"$
\n" ); document.write( " $\"x%28x%2B1%29%3E0\"$
\n" ); document.write( "Critical points 0 and -1.
\n" ); document.write( "Solutions: $\"x%3C-1\"$ OR $\"x%3E0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2-2x-1%3C0\"$
\n" ); document.write( "discriminant, 4-4(-1)=8
\n" ); document.write( "roots or horiz intercepts will be the critical points:
\n" ); document.write( " $\"x=%282-2sqrt%282%29%29%2F2=1-sqrt%282%29\"$
\n" ); document.write( "OR
\n" ); document.write( " $\"x=1%2Bsqrt%282%29\"$ .
\n" ); document.write( "The parabola opens upward, and the points below the level y=0 occur BETWEEN the horizontal intercepts.\r
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\n" ); document.write( "\n" ); document.write( "The x values common for both inequalities are $\"highlight%280%3Cx%3C1%2Bsqrt%282%29%29\"$ , which is easier to see if you make a number line. \n" ); document.write( "

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