document.write( "Question 210669: -3x≤3x+7≤½ \n" ); document.write( "
Algebra.Com's Answer #159176 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
\"-3x%3C=3x%2B7%3C=1%2F2\"
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document.write( "Note we can get two inequalities out of this:\r\n" );
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document.write( "\"highlight%28-3x%3C=3x%2B7%29%3C=1%2F2\"  AND \"-3x%3C=highlight%283x%2B7%3C=1%2F2%29\"\r\n" );
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document.write( "So we write:\r\n" );
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document.write( "\"-3x%3C=3x%2B7\" AND \"3x%2B7%3C=1%2F2\"\r\n" );
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document.write( "Add -3x to both sides of the first inequality.\r\n" );
document.write( "Multiply the second inequality through by 2 to\r\n" );
document.write( "clear of fractions:\r\n" );
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document.write( "\"-6x%3C=7\" AND \"6x%2B14%3C=1\"\r\n" );
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document.write( "Divide the first inequality through by \"-6\"\r\n" );
document.write( "which reverses the sign of inequality:\r\n" );
document.write( "Add \"-14\" to both sides of the second\r\n" );
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document.write( "\"x%3E=7%2F%28-6%29\" AND \"6x%3C=-13\"\r\n" );
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document.write( "Simplify the first and divide the second through\r\n" );
document.write( "by 6 (which BTW does not reverse the sign of\r\n" );
document.write( "inequality):\r\n" );
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document.write( "\"x%3E=-7%2F6\" AND \"x%3C=-13%2F6\"\r\n" );
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document.write( "It's easier to see if we change the\r\n" );
document.write( "improper fractions to mixed fractions\r\n" );
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document.write( "\"x%3E=-1%261%2F6\" AND \"x%3C=-2%261%2F6\"\r\n" );
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document.write( "As you can see this is a contradiction because\r\n" );
document.write( "the same value of x cannot be to the right of\r\n" );
document.write( "\"-1%261%2F6\"  AND also to the left of \"-2%261%2F6\".\r\n" );
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document.write( "Thus the solution set is the empty, or null, set, Ø\r\n" );
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document.write( "Edwin
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