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You can put this solution on YOUR website!
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\n" ); document.write( "The answer to the inequality log(x2-7x) < log(3-x) + log(2) is
\n" ); document.write( "(A) -1 < x < 0
\n" ); document.write( "(B) x > 7 or x < 0
\n" ); document.write( "(C) x > 7)
\n" ); document.write( "or -1 < x < 6
\n" ); document.write( "(D) -1 < x < 6
\n" ); document.write( "(E) -1 < x < 3
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document.write( "First, the domain for this inequality is the set of real numbers x such that\r\n" );
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document.write( " x^2 -7x > 0 and 3-x > 0, \r\n" );
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document.write( "or { x < 0 & x < 3 } U {x > 7 & x < 3 }.\r\n" );
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document.write( "Of the last two sets under the union sign, the second set {x > 7 & x < 3 } is empty; \r\n" );
document.write( "so, the domain is the set { x < 0 }. (1)\r\n" );
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document.write( "Next, the given inequality is equivalent to \r\n" );
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document.write( " log(x^2 -7x) < log (2(3-x))\r\n" );
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document.write( "which implies (due to the monotonicy of the logarithm function)\r\n" );
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document.write( " x^2 - 7x < 6 - 2x.\r\n" );
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document.write( "What follows, is the solution procedure for this inequality.\r\n" );
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document.write( " x^2 - 5x - 6 < 0,\r\n" );
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document.write( " (x-6)*(x+1) < 0.\r\n" );
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document.write( "The last inequality has the solution set { -1 < x < 6 }. (2)\r\n" );
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document.write( "To get the final answer, we shoud take the intersection of the set (2) with the domain set (1).\r\n" );
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document.write( "The intersection is the set { -1 < x < 0 }, or, in the interval form, (-1,0).\r\n" );
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document.write( "ANSWER. The solution to given inequality is the set { -1 < x < 0 }, or, in the interval form, (-1,0).\r\n" );
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document.write( "\r\n" ); document.write( "\n" ); document.write( "Solved, answered, and explained.\r
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\n" ); document.write( "\n" ); document.write( "I checked my solution visually, using plotting calculator www.desmos.com.\r
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\n" ); document.write( "\n" ); document.write( "Never write the optional answers all in one line: place each optional answer in separate line.\r
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\n" ); document.write( "\n" ); document.write( "I was forced to fix / (to re-edit) the entire your post.\r
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\n" ); document.write( "\n" ); document.write( "Now it makes sense, which it did not make before.\r
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