document.write( "Question 1183473: b <= 2a - 1
\n" ); document.write( "8 > a - b\r
\n" ); document.write( "\n" ); document.write( "According to the system of inequalities above, which of the following could be a value of a?\r
\n" ); document.write( "\n" ); document.write( "A. - 12
\n" ); document.write( "B. - 8
\n" ); document.write( "C. - 7
\n" ); document.write( "D. - 6
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Algebra.Com's Answer #813812 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
b <= 2a - 1
\n" ); document.write( "8 > a - b
\n" ); document.write( "According to the system of inequalities above, which of the following could be a value of a?
\n" ); document.write( "A. - 12
\n" ); document.write( "B. - 8
\n" ); document.write( "C. - 7
\n" ); document.write( "D. - 6
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document.write( "You are given two inequalities\r\n" );
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document.write( "    b <= 2a - 1        (1)\r\n" );
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document.write( "and\r\n" );
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document.write( "    8 > a - b.         (2)\r\n" );
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document.write( "This system of inequalities is equivalent to \r\n" );
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document.write( "    b <= 2a - 1        (3)\r\n" );
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document.write( "    b > a - 8          (4)\r\n" );
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document.write( "From (3) and (4), you have\r\n" );
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document.write( "    a - 8 < b <= 2a - 1,\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    a - 8 < 2a - 1.    (5)\r\n" );
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document.write( "Subtracting \"a\" from both sides of (5), you get\r\n" );
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document.write( "    - 8 < a - 1,\r\n" );
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document.write( "or\r\n" );
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document.write( "    - 8 + 1 < a,\r\n" );
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document.write( "      a > -7.\r\n" );
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document.write( "Having it, you see that options A), B) and C) do not work.\r\n" );
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document.write( "The option D) works.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "The solution by @MathLover1 has an error, and her answer is incorrect.\r
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\n" ); document.write( "\n" ); document.write( "The error is in the 9-th line from the top. Be aware.\r
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