Answer
$(−∞,-5/2)$ U $(9/4,∞)$
Work Step by Step
$(4x-9)(2x+5)>0$
$4x-9>0$
$4x-9+9>0+9$
$4x > 9$
$4x/4 > 9/2$
$ x > 9/4$
$2x+5 > 0$
$2x+5-5 > 0-5$
$2x > -5$
$2x/2 > -5/2$
$x > -5/2$
We have three sections: $(−∞,-5/2)$, $(-5/2, 9/4)$, and $(9/4,∞)$. We need to test one value for x in each section to determine if the section would be a solution set. Since we have the $0$
$(4(-5)-9)(2(-5)+5)>0$
$(-20-9)(-10+5)>0$
$-29*-5 >0$
$145 > 0$ (true)
$x=0$
$(4x-9)(2x+5)>0$
$(4*0-9)(2*0+5)>0$
$(0-9)(0+5) >0$
$-9*5 >0$
$-45 > 0$ (false)
$x=5$
$(4x-9)(2x+5)>0$
$(4*5-9)(2*5+5)>0$
$(20-9)(10+5)>0$
$11*15>0$
$165 > 0$ (true)
