Submodules via ideals

Suppose $R$ is a ring, $I\subseteq R$ is a left ideal, and $M$ is a left $R$-module. Let $IM\subseteq M$ denote the subset of all finite $I$-linear combinations in $M$, i.e., $$IM = \left{\sum_{\text{finite}} i_k m_k,\mid, i_k\in I,, m_k\in M\right}.$$ Prove $IM$ is a submodule of $M$.