Answer
$(−∞,-5/3)$ U $(7/2,∞)$
Work Step by Step
$(2x-7)(3x+5)>0$
$2x-7>0$
$2x-7+7>0+7$
$2x > 7$
$2x/2 > 7/2$
$ x > 7/2$
$3x+5 > 0$
$3x+5-5 > 0-5$
$3x > -5$
$3x/3 > -5/3$
We have five sections: $(−∞,-5/3)$, $(-5/3, 7/2)$, and $(7/2,∞)$. 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 $>$ sign, we exclude the end points and use parentheses instead of brackets.
Let $x=-5$, $x=0$, and $x=5$
$x=-5$
$(2x-7)(3x+5)>0$
$(2*-5-7)(3*-5+5)>0$
$(-10-7)(-15+5)>0$
$-17*-10 > 0$
$170 > 0$ (true)
$x=0$
$(2x-7)(3x+5)>0$
$(2*0-7)(3*0+5)>0$
$(0-7)(0+5)>0$
$-7*5>0$
$-35 >0$ (false)
$x=5$
$(2x-7)(3x+5)>0$
$(2*5-7)(3*5+5)>0$
$(10-7)(15+5)>0$
$3*20>0$
$60 >0$ (true)
