Continuous functions from $(X,d)$ to $(\mathbb{R},\mid\cdot\mid)$, open set

Question

If $f$,$g$ are continuous functions from $(X,d)$ to $(\mathbb{R},\mid\cdot\mid)$. Show that $A=\{x \in X : 2f(x) > 3g(x)\}$ is open in $X$.

I understand that the continuous image of an open set is open in the metric spaces and vice versa. But I need help in proving this assertion. Thank you.

Answer 1

$A =h^{-1}(0,\infty)$ where $h(x)=2f(x)-3g(x)$.