Solve For $x$ Given the Following Equation Involving a Determinant $$\left| \begin{array} { c c } x + 1 & 7 \\- 1 & x + 9\end{array} \right| = 0$$

Multiple Choice

Solve for $x$ given the following equation involving a determinant.
$$\left| \begin{array} { c c } x + 1 & 7 \\- 1 & x + 9\end{array} \right| = 0$$

A) $x = 8,2$
B) $x = - 9 , - 1$
C) $x = 9,1$
D) $x = - 8 , - 2$
E) $x = 8 , - 7$