document.write( "Question 1207692: Find a and b.\r
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\n" ); document.write( "\n" ); document.write( "If -3 < x < 3, then a < 1 - 2x < b. \n" ); document.write( "

Algebra.Com's Answer #845699 by ikleyn(52784) $\"\"$ $\"About$

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document.write( "Function  {1-2x}  is the monotonically decreasing function of x in the interval -3 < x < 3.\r\n" );
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document.write( "Therefore, we should take for \"a\" the value of the function 1-2x at the right end\r\n" );
document.write( "of the interval x = 3, i.e.  \r\n" );
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document.write( "    a = 1 - 2*3 = 1 - 6 = -5.\r\n" );
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document.write( "Respectively,  we should take for \"b\" the value of the function 1-2x at the left end\r\n" );
document.write( "of the interval x = -3, i.e.  \r\n" );
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document.write( "    b = 1 - 2*(-3) = 1 + 6 = 7.\r\n" );
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document.write( "ANSWER.  a = -5;  b = 7.\r\n" );
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document.write( "CHECK.  We should check if \r\n" );
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document.write( "    -5 < 1 - 2x < 7  at x in the interval (-3,3).   \r\n" );
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document.write( "        It is correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Comment from student: You are saying to equate a and b to 1 - 2x and solve individually. Yes?\r
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\n" ); document.write( "\n" ); document.write( "My response: Hello, you asked me to solve this problem for you.\r
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\n" ); document.write( "\n" ); document.write( "I did it and expressed it in a way which I found the most appropriate.\r
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\n" ); document.write( "\n" ); document.write( "Thus I said what I said in my post.\r
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\n" ); document.write( "\n" ); document.write( "To me, there is no need to re-tell it in other words.\r
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