Answer
$(-∞,-7/6)$ U $(12/7, ∞)$
Work Step by Step
$(6x+7)(7x-12)>0$
$6x+7>0$
$6x+7-7 >0-7$
$6x>-7$
$6x/6>-7/6$
$x > -7/6$
$7x-12>0$
$7x-12+12>0+12$
$7x>12$
$7x/7 > 12/7$
$x > 12/7$
We have three sections: $(-∞,-7/6)$, $(-7/6, 12/7)$, and $(12/7, ∞)$. 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 $x=-2$, $x=0$, and $x=3$
$x=-2$
$(6x+7)(7x-12)>0$
$(6*-2+7)(7*-2-12)>0$
$(-12+7)(-14-12)>0$
$-5*-26>0$
$130 >0$ (true)
$x=0$
$(6x+7)(7x-12)>0$
$(6*0+7)(7*0-12)>0$
$(0+7)(0-12)>0$
$7*-12>0$
$-84>0$ (false)
$x=3$
$(6x+7)(7x-12)>0$
$(6*3+7)(7*3-12)>0$
$(18+7)(21-12)>0$
$25*9>0$
$225 >0$ (true)
