To find the value of x for which the line passing through points F(3-2x, 12) and G(x + 9, 7) is vertical, we need to determine when the slope of the line is undefined.
The slope of a line can be calculated using the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
In this case, the change in x-coordinates is (x + 9) - (3 - 2x), which simplifies to 4x + 6.
The change in y-coordinates is 7 - 12, which is -5.
For a vertical line, the slope is undefined, which means the change in x-coordinates must be zero. Therefore, we set 4x + 6 = 0 and solve for x:
4x + 6 = 0
4x = -6
x = -6/4
x = -3/2
So, the value of x for which the line passing through points F(3-2x, 12) and G(x + 9, 7) is vertical is x = -3/2.