The functions $f$ and $g$ are defined as $f(x)=0.5x+7$ and $g(x)=1.5x-3$. If the function $h$ is defined as $h(x)=g(x)-f(x)$, what is the $x$-coordinate of the $x$-intercept of the graph of $y=h(x)$ in the $xy$-plane?