Expand `|(7x,6), (2x, 1)|`

Answer

To expand the determinant \(|(7x, 6), (2x, 1)|\), we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Determinant**:
We define the determinant \(\Delta\) as follows:
\[ \Delta = \begin{vmatrix} 7x & 6 \\ 2x & 1 \end{vmatrix} \]

2. **Apply the Determinant Formula**:
The formula for a 2x2 determinant is given by:
\[ \Delta = ad - bc \]
where \(a = 7x\), \(b = 6\), \(c = 2x\), and \(d = 1\).

3. **Substitute the Values**:
Substituting the values into the determinant formula:
\[ \Delta = (7x)(1) - (6)(2x) \]

4. **Simplify the Expression**:
Now, we simplify the expression:
\[ \Delta = 7x - 12x \]

5. **Combine Like Terms**:
Combine the terms:
\[ \Delta = -5x \]

### Final Result:
Thus, the expanded form of the determinant \(|(7x, 6), (2x, 1)|\) is:
\[ -5x \]