Answer: D) union
======================================================
Step-by-step explanation:
Let's solve the first inequality for x.
4x-5 ≥ 3
4x ≥ 3+5
4x ≥ 8
x ≥ 8/4
x ≥ 2
Now solve the other inequality
5 - x > 8
5 > 8+x
8+x < 5
x < 5-8
x < -3
The two solutions we get are x < -3 or x ≥ 2
These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.
Either x is smaller than -3, OR it is 2 or larger
I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.