Answer
$(-5/2, 9/4)$
Work Step by Step
$(4x-9)(2x+5)<0$
$(4x-9)(2x+5)=0$
$4x-9=0$
$4x=9$
$4x/4=9/4$
$x=9/4$
$2x+5=0$
$2x=-5$
$2x/2=-5/2$
$x=-5/2$
(-infinity, $-5/2)$
$(-5/2, 9/4)$
$(9/4$, infinity)
Let $x=-3$, $x=0$, $x=3$
$x=-3$
$(4x-9)(2x+5)<0$
$(4*-3-9)(2*-3+5)<0$
$(-12-9)(-6+5)<0$
$-21*-1<0$
$21<0$ (false)
$x=0$
$(4x-9)(2x+5)<0$
$(4*0-9)(2*0+5)<0$
$(0-9)(0+5)<0$
$-9*5<0$
$-45<0$ (true)
$x=3$
$(4x-9)(2x+5)<0$
$(4*3-9)(2*3+5)<0$
$(12-9)(6+5)<0$
$3*11<0$
$33<0$ (false)
