Your inequality
-7x > 1/15
can be solved by multiplying both sides by -1/7. Because this is a negative number, the direction of the inequality must be reversed.
(-1/7)(-7x) < (-1/7)(1/15)
x < -1/(7*15)
x < -1/105
-7x > 1/15
can be solved by multiplying both sides by -1/7. Because this is a negative number, the direction of the inequality must be reversed.
(-1/7)(-7x) < (-1/7)(1/15)
x < -1/(7*15)
x < -1/105