document.write( "Question 1087723: Solve the quadratic inequality. Write the solution set in interval notation. Show the complete solution.
\n" ); document.write( " 𝑥(𝑥+1)>112−5𝑥 \n" ); document.write( "

Algebra.Com's Answer #702026 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "x*(x+1) > 112 -5x,      ====> (equivalent transformation)  ====>  \r\n" );
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document.write( "x^2 + x > 112 - 5x,     ====> (equivalent transformation)  ====>  \r\n" );
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document.write( "x^2 +x + 5x - 112 > 0,  ====> (equivalent transformation)  ====>  \r\n" );
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document.write( "x^2 + 6x - 112 > 0.\r\n" );
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document.write( "Factor left side. You will get\r\n" );
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document.write( "(x+14)*(x-8) > 0,  or,  equivalently\r\n" );
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document.write( "(x-(-14)*(x-8) > 0.    (1)\r\n" );
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document.write( "1)  If  x < -14  then each factor in the left side of (1) is negative,\r\n" );
document.write( "    so the product is positive.\r\n" );
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document.write( "2)  If  -14 < x < 8  then the factor (x-(-14)) is positive, while the factor (x-8) in the left side of (1) is negative,\r\n" );
document.write( "    so the product is negative.\r\n" );
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document.write( "3)  If 8 < x  then each factor in the left side of (1) is positive,\r\n" );
document.write( "    so the product is positive.\r\n" );
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document.write( "Answer.  The given inequality has  the union of segments  (,}}}] U [,) as the solution set.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to learn on how to solve quadratic inequalities, read the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving problems on quadratic inequalities \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Inequalities\".\r
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