document.write( "Question 1202031: Solve the following inequality for x:
\n" ); document.write( "2x^2 + 5x < 3: \n" ); document.write( "

Algebra.Com's Answer #836646 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Solve the following inequality for x:
\n" ); document.write( "2x^2 + 5x < 3:
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The solution by @mananth is incorrect.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The starting inequality is \r\n" );
document.write( "\r\n" );
document.write( "    2x^2 + 5x < 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Reduce to the standard quadratic inequality form\r\n" );
document.write( "\r\n" );
document.write( "    2x^2 + 5x - 3 < 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factirize left side\r\n" );
document.write( "\r\n" );
document.write( "    (x+3)*(2x-1) < 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The roots of the quadratic function in the left side are -3 and 1/2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The parabola is below the x-axis between the roots.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the solution to the given inequality is this set of real numbers\r\n" );
document.write( "\r\n" );
document.write( "     { -3 < x < 1/2 }, or in the interval form  (-3,1/2).    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );