The first inequality given is:
5x - 11 < -11
5x < -11 + 11
5x < 0
x < 0
This means that : x ∈ ]-∞,0[
The second inequality given is:
4x + 2 > 14
4x > 14-2
4x > 12
x > 3
This means that:
x ∈ ]3,∞[
Since the two inequalities are linked by an "or", this means that the solution is the union of the two intervals:
x ∈ ]-∞,0[ U ]3,∞[