The expression you've provided seems to involve finding the value of \( x \) such that the determinant of a matrix is zero. The matrix can be interpreted as:

\[
\begin{pmatrix}
x & 8 \\
3 & 3
\end{pmatrix}
\]

To find the value of \( x \), we'll compute the determinant of the matrix and set it equal to zero.

The determinant of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) is calculated as:

\[
\text{Determinant} = ad - bc
\]

For the given matrix:

\[
\text{Determinant} = x \cdot 3 - 8 \cdot 3 = 3x - 24
\]

Setting the determinant equal to zero:

\[
3x - 24 = 0
\]

Solve for \( x \):

\[
3x = 24
\]

\[
x = \frac{24}{3} = 8
\]

So, the value of \( x \) is \( \boxed{8} \).

Would you like more details on any of the steps or concepts used? Here are some related questions to consider:

1. What is the general formula for the determinant of a 3x3 matrix?
2. How does the determinant relate to the area (or volume) in geometry?
3. Can a matrix with a determinant of zero be inverted?
4. What is the significance of the determinant in solving systems of linear equations?
5. How would the determinant change if the entries of the matrix were functions of \( x \)?

**Tip:** A determinant of zero for a square matrix indicates that the matrix is singular, meaning it does not have an inverse.

Learn how to find the value of x in a matrix determinant problem. This problem involves computing the determinant of a 2x2 matrix and solving for x. Suitable for advanced high school students.

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