## Precalculus (6th Edition) Blitzer

The value of $x$ is $-11$.
Consider, $\left| \begin{matrix} -2 & x \\ 4 & 6 \\ \end{matrix} \right|=32$ Calculate the above determinant as given: $\left| \begin{matrix} -2 & x \\ 4 & 6 \\ \end{matrix} \right|=32$ This implies that, $\left( -2\times 6 \right)-\left( 4\times x \right)=32$ Simplify the above equation, $-12-4x=32$ Add 12 to both sides to get, $-4x=44$ Divide by $-4$. Then, $x=-11$. Hence, $x=-11$.