Answer
The inequality is valid for values between -0.5 and 3 (not including them) i.e. $(-0.5,3)$
Work Step by Step
First, we are going to set the right side to zero and factor to find the x-intercepts:
$2x^2-5x-3=0$
$(2x+1)(x-3)=0$
$x_1=-0.5$
$x_2=3$
These are the critical points. We are going to take three values: one less than -0.5, one between -0.5 and 3, and one more than 3 to test in the original equation and check if the inequality is true or not:
First test with a value less than -0.5:
$2(-1)^2<5(-1)+3$
$2
