Verified answer

(x + 9)/(x - 7) < 1

(x + 9)/(x - 7) - 1 < 0

(x + 9 - x + 7)/(x - 7) < 0

16/(x - 7) < 0

x < 7

(9x + 9)/(6x -5) > -1

(9x + 9)/(6x -5) + 1 > 0

(9x + 9 + 6x - 5)/(6x - 5) > 0

(15x + 4)/(6x - 5) > 0

++++++(-4/15) --------- (5/6) +++++++

x∈(-∞, -4/15) U (5/6, +∞)

пересекаем с 1

x∈(-∞, -4/15) U (5/6, +7)