document.write( "Question 56935: -2|3j|-8 is less than or equal to -20 \n" ); document.write( "
Algebra.Com's Answer #38692 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
-2|3j| - 8 < -20\r\n" );
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document.write( "Isolate the absolute value term by adding +8 to both \r\n" );
document.write( "sides:\r\n" );
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document.write( " -2|3j| - 8 < -20\r\n" );
document.write( "        + 8   + 8\r\n" );
document.write( "-------------------\r\n" );
document.write( " -2|3j|     < -12\r\n" );
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document.write( "Divide both sides by -2, to leave just the absolute value\r\n" );
document.write( "on the left.  Here we must reverse the inequality < to >\r\n" );
document.write( "because we divided by a negative number. [When dividing\r\n" );
document.write( "by a positive number we never reverse the inequality but\r\n" );
document.write( "when dividing by a negative number, as we are doing here,\r\n" );
document.write( "we always reverse it.]\r\n" );
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document.write( "  -2|3j|      -12\r\n" );
document.write( " --------  > -----\r\n" );
document.write( "    -2         -2\r\n" );
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document.write( "Simplifying,\r\n" );
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document.write( "      |3j| > 6\r\n" );
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document.write( "We can take a positive factor outside an absolute value\r\n" );
document.write( "so we can take out 3\r\n" );
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document.write( "      3|j| > 6\r\n" );
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document.write( "Divide both sides by 3. We DO NOT reverse the inequality\r\n" );
document.write( "this time because we are dividing both sides by a\r\n" );
document.write( "positive number, 3.\r\n" );
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document.write( "      |j| > 6\r\n" );
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document.write( "This means that j can be any number which is 6 or more\r\n" );
document.write( "units away from 0 on the number line.  j can be either\r\n" );
document.write( "6 or more units away from 0 on the lower side or 6 or\r\n" );
document.write( "more units away from 0 on the upper side of 0.  So the\r\n" );
document.write( "graph looks like this\r\n" );
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document.write( "<==========]-----------------------[===========>\r\n" );
document.write( " -10  -8  -6  -4  -2   0   2   4   6   8  10 12  \r\n" );
document.write( "    \r\n" );
document.write( "      j < -6  OR  j > 6\r\n" );
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document.write( "and the interval notation for the solution is\r\n" );
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document.write( "     (-¥, -6] È [6, ¥)\r\n" );
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document.write( "Edwin
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