Problem 2

Explanation

We are given a determinant equation of $2 \times 2$ matrices. Recall that the formula for the determinant of a matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is $ad - bc$.

Calculating the Left Hand Side Determinant

First, we calculate the determinant of the matrix on the left side:

Calculating the Right Hand Side Determinant

Next, we calculate the determinant of the matrix on the right side which contains the variable $x$:

Determining the Variable Value

Now we equate both determinant results according to the original equation:

Divide both sides by 10 to find the value of $x$:

Thus, the value of $x$ that satisfies the equation is -3.