Question about comaximal ideal proof

Question

Let $A$ be a ring and $M\subseteq A$ a maximal ideal. Show that if $I\subseteq A$ such that $I\not\subseteq M$, then $M$ and $I$ are comaximal($M+I=A$).

I cannot find the proof for this statement.

Answer 1

$M+I$ is by definition an ideal, it contains $M$, and since $I \not\subseteq M$, it strictly contains $M$. Since $M$ is maximal, it follows that $I+M=A$.