Weights of a representation of a semisimple Lie algebra

Question

Suppose we have a semisimple Lie algebra $\mathfrak{g}$, a simple $\mathfrak{g}$-module $V(\lambda)$, a weight $\mu$ of $V(\lambda)$, and a root $\alpha$.

Is it true that if $\mu+\alpha$ is not a weight of $V(\lambda)$ then $(\alpha,\mu) \geq 0$?