solving for scalar involving matrix equations

Question

consider following matrix equation

$\boldsymbol{1}^T \Sigma^{-1} ( \bar{\textbf{x}} - n \boldsymbol{1}. c) = 0 $

here $\boldsymbol{1} , \bar{\textbf{x}}$ are vectors of dimension $n \times 1$ and $\Sigma$ is invertible matrix of dimension $n \times n$ and n,c are constants

is there any way to solve it for scalar c ?

$\boldsymbol{1}^T \Sigma^{-1}\bar{\textbf{x}} = (n.c)\boldsymbol{1}^T \Sigma^{-1}\boldsymbol{1}$

and I am struck at here

Answer 1

$$c = \frac{ \boldsymbol{1}^T \Sigma^{-1}\bar{\textbf{x}} }{ n \boldsymbol{1}^T \Sigma^{-1}\boldsymbol{1} }.$$

Remember that $\boldsymbol{1}^T \Sigma^{-1}\boldsymbol{1}$ and $\boldsymbol{1}^T \Sigma^{-1}\bar{\textbf{x}}$ are scalars.