we have the inequality
5+10(x-9) < -103-(7-5x)
solve for x
apply distributive property left side and remove the parenthesis right side
5+10x-90 < -103-7+5x
Combine like terms
10x-85 < 5x-110
Group terms
10x-5x < -110+85
5x < -25
x< -25/5
x < -5
the solution is the interval (-inf, -5)
set builder notation
x| x < -5