How to determine which equality sign to use for $x(2x+7) > 0$ Express $x(2x+7)>0$ in interval notation. How do you determine which sign to use for the answer? Here is what I did,
$2x+7>0$ and $x>0$. I understand $x>0$ but why is $x<-\dfrac{2}{7}$? Shouldn't the sign be greater than because I am dividing by $2$ and not $-2$? Or does the $-7$ affect the sign as well?

There are two cases, because $ab>0$ if and only if $a>0$ and $b>0$, or $a<0$ and $b<0$. If $x>0$, then automatically $2x+7>0$, so $x(2x+7)>0$, and you have a solution. However, there are also solutions when $x<0$ and $2x+7<0$. Here the stronger constraint is the second one: if $2x+7<0$, then $2x<-7$, and $x<-\frac72$ (not $-\frac27$), in which case it’s certainly true that $x<0$ and hence that $x(2x+7)>0$.
In other words, every $x>0$ is a solution, but so is every $x<-\frac72$.
