document.write( "Question 924615: \"Describe how to use an absolute-value inequality to find all the values on a number line that are within 5 units of -6.\" \n" ); document.write( "
Algebra.Com's Answer #560996 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"The DISTANCE is the DISTANCE (in absolute value)\"\r\n" );
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document.write( "-15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "Let x be a variable that can take on any value that is within 5 units of -6.\r\n" );
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document.write( "Then the DISTANCE from any value of x to -6 is the DIFFERENCE (in absolute\r\n" );
document.write( "value.  The DIFFERENCE is x-(-6) and in absolute value is |x-(-6)| and we\r\n" );
document.write( "can simplify that to |x+6| and to make that distance (difference) less that\r\n" );
document.write( "5 units we write  \r\n" );
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document.write( "|x+6| < 5\r\n" );
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document.write( "You can also do it by starting with the inequality looking at the\r\n" );
document.write( "number line above: \r\n" );
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document.write( "-11 < x < -1 \r\n" );
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document.write( "Then add the opposite of -6, which is +6 to all three sides:\r\n" );
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document.write( "-11+6 < x+6 < -1+6\r\n" );
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document.write( "   -5 < x+6 < 5\r\n" );
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document.write( "       |x+6| < 5\r\n" );
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document.write( "Edwin
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