Answer
During the interval: $(30, +\infty)$
$x>30$
Work Step by Step
We can find the range of distances by at first calculating the distance at key point of $500°C$ :
$500=\frac{600,000}{x^2+300}$
$x^2+300=\frac{600,000}{500}$
$x^2=1200-300$
$x^2=900$
$x=30 $ $meters$
(In general, $x$ would be $±30$ but in this case $x$ represents distance, which cannot be negative. So we omit it)
It is a decreasing function, the temperature decreases as the distance increases, so the temperature would decrease when $x$ is greater than $30$. That means interval $(30, +\infty)$
$x>30$
Using almost the same idea, we could also write:
$T<500$
$\frac{600,000}{x^2+300}<500$
$x^2+300>\frac{600,000}{500}$
$x^2>1200-300$
$x^2>900$
$x>30 $
