Question:

The determinant is given by: 3(2x+2) - 4(x-1) = 0. Expanding this: 6x + 6 - 4x + 4 = 0. Simplifying: 2x + 10 = 0, which gives 2x = -10, so x = -5. Wait, checking the provided answer key for question 2 in Exercise (0-1) which is 'A'. Let's re-evaluate: 3(2x+2) - 4(x-1) = 0 => 6x + 6 - 4x + 4 = 0 => 2x + 10 = 0 => x = -5. Looking at the options, none match. Let's re-read the determinant: | 3 4 | | x-1 2x+2 | = 0. Wait, the image shows | 3 4 | | x-1 2x+2 | | 5 9 | = 0. This is a 3x2 matrix? No, it's likely a typo in the question image or it's meant to be a 2x2 determinant. If it's | 3 4 | | x-1 2x+2 | = 0, then 3(2x+2) - 4(x-1) = 0 => 6x+6-4x+4=0 => 2x+10=0 => x=-5. If the determinant is | 3 4 | | 5 9 | = 27-20=7, which is not 0. Perhaps it is | 3 4 | | x-1 2x+2 | = 0. Let's re-examine the image. It looks like | 3 4 | | x-1 2x+2 | = 0. The answer key says A (which is 3). If x=3, 3(2(3)+2) - 4(3-1) = 3(8) - 4(2) = 24 - 8 = 16 != 0. Let's re-read the determinant: | 3 4 | | x-1 2x+2 | = 0. Maybe it's | 3 x-1 | | 4 2x+2 | = 0? 3(2x+2) - 4(x-1) = 6x+6-4x+4 = 2x+10=0 => x=-5. There might be a typo in the question or the answer key.