Is it true that for any $x \in \mathbb{R}$ for all $q \in \mathbb{N}$, there exists a $\frac{p}{q} \in \mathbb{Q} : |x-\frac{p}{q}|< \frac{1}{q^2}$?

Question

Is there a result along the lines of :

For any $x \in \mathbb{R}$ for all $q \in \mathbb{N}$, there exists a $\frac{p}{q} \in \mathbb{Q} : |x-\frac{p}{q}|< \frac{1}{q^2}$.

Thanks for any help!