Question 1202031
.
Solve the following inequality for x:
2x^2 + 5x < 3:
~~~~~~~~~~~~~~~~~~~~~~~~



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution by @mananth is incorrect.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring a correct solution.



<pre>
The starting inequality is 

    2x^2 + 5x < 3.


Reduce to the standard quadratic inequality form

    2x^2 + 5x - 3 < 0.


Factirize left side

    (x+3)*(2x-1) < 0.


The roots of the quadratic function in the left side are -3 and 1/2.


The parabola is below the x-axis between the roots.


So, the solution to the given inequality is this set of real numbers

     { -3 < x < 1/2 }, or in the interval form  (-3,1/2).    <U>ANSWER</U>
</pre>

Solved.