document.write( "Question 550593: Solve the absolute valye inequality and graph your solution on a number line.\r
\n" ); document.write( "\n" ); document.write( "1. |x +3| < 4\r
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Algebra.Com's Answer #358904 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "To remove the absolute value bars of\r\n" );
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document.write( "      |Ax + B| < C  , where C is a positive number, write this:\r\n" );
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document.write( "    \r\n" );
document.write( "        -C < Ax + B < C\r\n" );
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document.write( "Then solve that for x in the middle.  The solution set will\r\n" );
document.write( "usually be of the form:\r\n" );
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document.write( "            (D, E) \r\n" );
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document.write( "Your example 4:\r\n" );
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document.write( "          |2x + 1| < 5\r\n" );
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document.write( "      -5 < 2x + 1 < 5\r\n" );
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document.write( "Add -1 to all three sides:\r\n" );
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document.write( "        -6 < 2x < 4\r\n" );
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document.write( "Divide through by 2 (That will NOT reverse the < signs)\r\n" );
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document.write( "         -3 < x < 2\r\n" );
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document.write( "Graph:\r\n" );
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document.write( "---------o===================o--------\r\n" );
document.write( "-5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "Interval notation:\r\n" );
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document.write( "         (-3, 2)\r\n" );
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document.write( " [x] +6 < 10\r\n" );
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document.write( "Your example 6:\r\n" );
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document.write( "          |x| + 6 < 10\r\n" );
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document.write( "Isolate the |x| by subtracting 6 from both sides:\r\n" );
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document.write( "             |x| < 4\r\n" );
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document.write( "           -4 < x < 4\r\n" );
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document.write( "Graph:\r\n" );
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document.write( "-----o===============================o--------\r\n" );
document.write( "-5  -4  -3  -2  -1   0   1   2   3   4   5   6\r\n" );
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document.write( "Interval notation:\r\n" );
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document.write( "         (-4, 4)\r\n" );
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document.write( "---------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "To remove the absolute value bars of\r\n" );
document.write( "\r\n" );
document.write( "      |Ax + B| > C  , where C is a positive number, write this:\r\n" );
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document.write( "    \r\n" );
document.write( "   Ax + B < -C  OR  Ax + B > C\r\n" );
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document.write( "Then solve that for x in each part, leaving the word \"OR\" between them\r\n" );
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document.write( "The solution usually will be of this form:\r\n" );
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document.write( "      (, D) U (E, )\r\n" );
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document.write( "Your example 2:\r\n" );
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document.write( "              |x - 5| > 2 \r\n" );
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document.write( "       x - 5 < -2 OR x - 5 > 2\r\n" );
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document.write( "Add 5 to borth sides of both parts:\r\n" );
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document.write( "            x < 3 OR x > 7\r\n" );
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document.write( "Graph:\r\n" );
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document.write( "<====================o---------------o===========>\r\n" );
document.write( "-2  -1   0   1   2   3   4   5   6   7   8   9  10\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "     (, 3) U (7,)\r\n" );
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document.write( "Edwin

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