#### Answer

$(-1,\frac{7}{2})$

#### Work Step by Step

$2x^2-5x\lt7$ Write as an equation.
$2x^2-5x-7=0$ Factor by grouping.
$(x+1)(2x-7)=0$ Solve as an equation.
$x=-1$
$x=\frac{7}{2}$
Plot these numbers on a number line,split them into intervals, take one test point from each interval, and check them to see if they are true. If they are true, then it is a solution.
In this case, it is
$(-1,\frac{7}{2})$