Trying to solve problem

-7x> - 2(x - 30<10
-7x> - 2x - 30 <10
-7x + 2x > -30<10
-5x>-30<10
-5x/-5 > -30/-5
x>6<10
is this correct?

I see a problem in the first line,

-7x> - 2(x - 30<10 has no closing brackets.
In your third line your work shows that there was no need for a bracket.

secondly, in a compound inequality the direction of the signs should be the same,
e.g.
-3 < x < 5
and the two parts can be split using AND as a logic operator

applying this to yours would give me:

-7x > -2x-30 AND -2x-30 < 10
-5x > -30 AND -2X < 40
x < 6 AND x > 20
which would be "no solution"

I will let you fix it and then we'll see