document.write( "Question 789839: Solve for 3 < |x+2| < 8 and graph the solution set\r
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Algebra.Com's Answer #478955 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "3 < |x+2| < 8\r\n" );
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document.write( "Case 1:  x+2 >= 0 which is equialent to x >= -2\r\n" );
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document.write( "3 < x+2 < 8\r\n" );
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document.write( "Subtract 2 from all three sides:\r\n" );
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document.write( "1 < x < 6 which is compatible with x >= -2\r\n" );
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document.write( "1 < x < 6 in interval notation is (1,6)\r\n" );
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document.write( "Part of the graph is\r\n" );
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document.write( "----------o===================o----------------------------------------------------\r\n" );
document.write( "-13 -12 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8\r\n" );
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document.write( "Case 2:  x+2 < 0 which is equivalent to x < -2\r\n" );
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document.write( "3 < -x-2 < 8\r\n" );
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document.write( "Add 2 to all three sides:\r\n" );
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document.write( "5 < -x < 10\r\n" );
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document.write( "Divide all three sides by -1 which causes\r\n" );
document.write( "the inequality signs to reverse:\r\n" );
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document.write( "-5 > x > -10\r\n" );
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document.write( "which is the same as\r\n" );
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document.write( "-10 < x < -5 which is compatible with x < -2\r\n" );
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document.write( "-10 < x < -5 in interval notation is (-10,-5)\r\n" );
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document.write( "Graph of solution:\r\n" );
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document.write( "----------o===================o-----------------------o===================o--------\r\n" );
document.write( "-13 -12 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8\r\n" );
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document.write( "Solution in set builder notation {x|-10 < x < -5 OR 1 < x < 6}\r\n" );
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document.write( "Solution in interval notation: (-10,-5) U (1,6) \r\n" );
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document.write( "Edwin

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