Your sign chart is a bit off. The first two rows are correct. However keep in mind that you factored out a negative (when you factored -2x+14) so you need to negate the signs of the f(x) row.
Another thing to keep in mind: x = 4 is not allowed as its the vertical asymptote. However, x = 7 is valid. So you'll have an open circle at x = 4 and a close circle at x = 7
The answer in interval notation is (-infinity, 4) U [7, infinity)
which translates to this disjoint set of inequalities: x < 4 or x >= 7
