Many-one reduction from inequality problem to equality problem
The following should yield a many-one reduction from $M_{ineq}$ to $M_{eq}$:

Given $G=(V,E)$ and $k$ construct $G'$ with


vertex set $V \times \{1,\dots,k\}$ and
edges between $(v,i)$ and $(w,j)$ if


(1) $i=j$ or
(2) $v=w$ or
(3) $(v,w) \in E$.

Because of (1), no independent set can be larger than $k$ (as all vertices in the same slice are connected). Because of (2) and (3) each independent set in $G'$ induces an independent set of $G$ and vice versa, therefore $G$ has an ind. set of size $\ge k$ if and only if $G'$ has an independent set of size exactly $k$.