One-sided Dirichlet approximation

Question

A version of Dirichlet's Theorem states: Given $d \in \mathbb{R}$ and an integer $N \geq 2$, there exist integers $p$ and $q$ with $p > 0$ such that $$ |pd - q | \leq \frac{1}{N}.$$ Is the result also true for the version without the absolute value? In other words, do there exist integers $p$ and $q$ with $p > 0$ such that $$ 0 \leq pd - q \leq \frac{1}{N}?$$