document.write( "Question 1139541: Solve the system of inequalities and indicate all the integers which are in the solution set:\r
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Algebra.Com's Answer #760029 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The \"solution\" by @josgarithmetic is totally wrong.\r
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\n" ); document.write( "\n" ); document.write( " So I came to bring a correct solution.\r
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document.write( "You have this system\r\n" );
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document.write( "    2 - 6y < 14,       (1)\r\n" );
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document.write( "    1 < 21 - 5y.       (2)\r\n" );
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document.write( "By default, it means that you should find the solution set to each inequality SEPARATELY, \r\n" );
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document.write( "and then take the common part of these two sets, i.e. the intersection of the separate solution sets.\r\n" );
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document.write( "OK. Let' start from the first inequality\r\n" );
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document.write( "1)    2 - 6y < 14  is equivalent to  2 - 14 < 6y,   -12 < 6y,   y >  = -2.\r\n" );
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document.write( "      Thus { y > -2 }  is the solution set to the first inequality.\r\n" );
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document.write( "Next, let's solve the second inequality\r\n" );
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document.write( "2)    1 < 21 - 5y  is equivalent to  5y < 21 - 1,   5y < 20,   y <  = 4.\r\n" );
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document.write( "      Thus { y < 4 }  is the solution set to the second inequality.\r\n" );
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document.write( "3)    Now, the solution to the given system is the common part of the two solution sets, \r\n" );
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document.write( "      i.e. their intersection, which is the interval  (-2,4).\r\n" );
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document.write( "ANSWER.  The solution to the given system is the set  -2 < x < 4, or, which is the same, the interval (-2,4).\r\n" );
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document.write( "         The integers in this interval are -1, 0, 1, 2, 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problem on systems of inequalities in one variable, see my lessons \r
\n" ); document.write( "\n" ); document.write( " - Solving systems of linear inequalities in one unknown \r
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\n" ); document.write( "\n" ); document.write( "From these lessons, learn the subject once and for all.\r
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