SOLUTION: Solve the following inequality for x: 2x^2 + 5x < 3:

Algebra.Com
Question 1202031: Solve the following inequality for x:
2x^2 + 5x < 3:
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
2x^2 + 5x < 3
2x^2+5x-3<0
factorise
2x^2+6x-x-3<0
2x(x+3)-1(x+3)<0
(x+3)(x-1) <0
-3
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
Solve the following inequality for x:
2x^2 + 5x < 3:
~~~~~~~~~~~~~~~~~~~~~~~~


            The solution by @mananth is incorrect.
            I came to bring a correct solution. 


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).    ANSWER

Solved.



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