If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.
- \(x = 3, -2\)
- \(x = 4, \frac{-2}{3}\)
- \(x = -4, \frac{3}{2}\)
-
\(x = 4, \frac{-3}{2}\)
The correct answer is: D
Explanation
\(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \implies (1+2x)(3-x) - (-6) = -3\)
\(3 - x + 6x - 2x^{2} + 6 = -3\)
\(-2x^{2} + 5x + 3 + 6 + 3 = 0\)
Multiplying through with -1,
\(2x^{2} - 5x -12 = 0\)
\((2x + 3)(x - 4) = 0 \implies x = \frac{-3}{2} , 4\)