If `|(2x,5),(8,x)|=|(6,-2),(7,3)|` then the value of `x` is

Options

A. `3`
B. `+-3`
C. `+-6`
D. `6`

Explanation

To solve the equation \( |(2x, 5), (8, x)| = |(6, -2), (7, 3)| \), we will calculate the determinants of both matrices and set them equal to each other.

### Step 1: Calculate the determinant of the first matrix
The first matrix is:
\[ \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} \]
The determinant of a \(2 \times 2\) matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) is given by \(ad - bc\).

For our matrix:
\[ \text{Determinant} = (2x)(x) - (5)(8) = 2x^2 - 40 \]

### Step 2: Calculate the determinant of the second matrix
The second matrix is:
\[ \begin{pmatrix} 6 & -2 \\ 7 & 3 \end{pmatrix} \]
Calculating its determinant:
\[ \text{Determinant} = (6)(3) - (-2)(7) = 18 + 14 = 32 \]

### Step 3: Set the determinants equal to each other
Now we set the two determinants equal:
\[ 2x^2 - 40 = 32 \]

### Step 4: Solve for \(x\)
Rearranging the equation:
\[ 2x^2 - 40 - 32 = 0 \\ 2x^2 - 72 = 0 \\ 2x^2 = 72 \\ x^2 = 36 \]

Taking the square root of both sides:
\[ x = \pm 6 \]

### Final Answer
Thus, the value of \(x\) is:
\[ x = 6 \quad \text{or} \quad x = -6 \]

---