document.write( "Question 289387: The absolute value of $\"+1-+1%2Fx+\"$ is less than and equal to 3. Solve the inequality, express your answer in interval notation. \n" ); document.write( "
Algebra.Com's Answer #209622 by Edwin McCravy(20059) $\"\"$ $\"About$
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document.write( "We find the critical values by solving the boundary equation:\r\n" );
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document.write( "Which breaks into these two equations:\r\n" );
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document.write( "  or \r\n" );
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document.write( "   or \r\n" );
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document.write( "    or \r\n" );
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document.write( "   or \r\n" );
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document.write( "We also have a third critical value x=0 because\r\n" );
document.write( "that is what we get when we set the denominator\r\n" );
document.write( "in the original problem = 0.  \r\n" );
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document.write( "So we put those points on a number line\r\n" );
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document.write( "----------------o----o--o------------------\r\n" );
document.write( "-2       -1   -1/2   0 1/4      1         2\r\n" );
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document.write( "We test a value left of -1/2, say -1, in the\r\n" );
document.write( "original inequality:\r\n" );
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document.write( "That's true, so we shade the region left of -1/2\r\n" );
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document.write( "<================o----o--o------------------\r\n" );
document.write( " -2       -1   -1/2   0 1/4      1         2\r\n" );
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document.write( "We test a value between -1/2 and 0, say -.2 in the\r\n" );
document.write( "original inequality:\r\n" );
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document.write( "That's false, so we DO NOT shade the region between\r\n" );
document.write( "-1/2 and 0\r\n" );
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document.write( "We test a value between 0 and 1/4, say .2 in the\r\n" );
document.write( "original inequality:\r\n" );
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document.write( "That's false, so we DO NOT shade the region between\r\n" );
document.write( "0 and 1/4.\r\n" );
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document.write( "We test a value right of 1/4, say 1, in the\r\n" );
document.write( "original inequality:\r\n" );
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document.write( "That's true so we shade -1/2\r\n" );
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document.write( "<================@----o--o=================>\r\n" );
document.write( " -2       -1   -1/2   0 1/4      1         2\r\n" );
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document.write( "Now we test the endpoint 1/4\r\n" );
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document.write( "That's true so we shade 1/4\r\n" );
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document.write( "<================@----o--@=================>\r\n" );
document.write( " -2       -1   -1/2   0 1/4      1         2\r\n" );
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document.write( "So the solution set is:\r\n" );
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document.write( "Edwin
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